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

Percentage Accurate: 68.4% → 86.5%

Time: 8.8s

Alternatives: 15

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 86.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.3 \cdot 10^{+77} \lor \neg \left(z \leq 2.2 \cdot 10^{+126}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{-\left(t - x\right)}{z}, y - a, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a - z}, y - z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.3e+77) (not (<= z 2.2e+126)))
   (fma (/ (- (- t x)) z) (- y a) t)
   (fma (/ (- t x) (- a z)) (- y z) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.3e+77) || !(z <= 2.2e+126)) {
		tmp = fma((-(t - x) / z), (y - a), t);
	} else {
		tmp = fma(((t - x) / (a - z)), (y - z), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.3e+77) || !(z <= 2.2e+126))
		tmp = fma(Float64(Float64(-Float64(t - x)) / z), Float64(y - a), t);
	else
		tmp = fma(Float64(Float64(t - x) / Float64(a - z)), Float64(y - z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.3e+77], N[Not[LessEqual[z, 2.2e+126]], $MachinePrecision]], N[(N[((-N[(t - x), $MachinePrecision]) / z), $MachinePrecision] * N[(y - a), $MachinePrecision] + t), $MachinePrecision], N[(N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.2999999999999998e77 or 2.19999999999999999e126 < z

   1. Initial program 30.5%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

      9. distribute-rgt-out-- N/A

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

      10. distribute-lft-neg-in N/A

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 86.8%

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

   if -8.2999999999999998e77 < z < 2.19999999999999999e126

   1. Initial program 81.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 89.9

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

   4. Applied rewrites 89.9%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.3 \cdot 10^{+77} \lor \neg \left(z \leq 2.2 \cdot 10^{+126}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{-\left(t - x\right)}{z}, y - a, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a - z}, y - z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 75.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{-\left(t - x\right)}{z}, y - a, t\right)\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-225}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- (- t x)) z) (- y a) t)))
   (if (<= z -4.6e+40)
     t_1
     (if (<= z -4.2e-225)
       (+ x (/ (* (- y z) t) (- a z)))
       (if (<= z 9.8e+33) (fma (- y z) (/ (- t x) a) x) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((-(t - x) / z), (y - a), t);
	double tmp;
	if (z <= -4.6e+40) {
		tmp = t_1;
	} else if (z <= -4.2e-225) {
		tmp = x + (((y - z) * t) / (a - z));
	} else if (z <= 9.8e+33) {
		tmp = fma((y - z), ((t - x) / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(-Float64(t - x)) / z), Float64(y - a), t)
	tmp = 0.0
	if (z <= -4.6e+40)
		tmp = t_1;
	elseif (z <= -4.2e-225)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	elseif (z <= 9.8e+33)
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[((-N[(t - x), $MachinePrecision]) / z), $MachinePrecision] * N[(y - a), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[z, -4.6e+40], t$95$1, If[LessEqual[z, -4.2e-225], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e+33], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.59999999999999987e40 or 9.80000000000000027e33 < z

   1. Initial program 39.6%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

      9. distribute-rgt-out-- N/A

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

      10. distribute-lft-neg-in N/A

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 82.5%

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

   if -4.59999999999999987e40 < z < -4.20000000000000001e-225

   1. Initial program 86.9%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 77.1

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

   5. Applied rewrites 77.1%

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

   if -4.20000000000000001e-225 < z < 9.80000000000000027e33

   1. Initial program 84.4%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 88.1

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

   5. Applied rewrites 88.1%

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

Alternative 3: 65.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \mathbf{if}\;z \leq -5.1 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{+33}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- t x) z) a t)))
   (if (<= z -5.1e+151)
     t_1
     (if (<= z -1.65e+33)
       (* (- y z) (/ t (- a z)))
       (if (<= z 2.9e+76) (fma (- t x) (/ y a) x) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((t - x) / z), a, t);
	double tmp;
	if (z <= -5.1e+151) {
		tmp = t_1;
	} else if (z <= -1.65e+33) {
		tmp = (y - z) * (t / (a - z));
	} else if (z <= 2.9e+76) {
		tmp = fma((t - x), (y / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(t - x) / z), a, t)
	tmp = 0.0
	if (z <= -5.1e+151)
		tmp = t_1;
	elseif (z <= -1.65e+33)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	elseif (z <= 2.9e+76)
		tmp = fma(Float64(t - x), Float64(y / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * a + t), $MachinePrecision]}, If[LessEqual[z, -5.1e+151], t$95$1, If[LessEqual[z, -1.65e+33], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+76], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.09999999999999996e151 or 2.9000000000000002e76 < z

   1. Initial program 29.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 50.7

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

   4. Applied rewrites 50.7%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

   7. Applied rewrites 73.3%

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

   8. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r* N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. mul-1-neg N/A

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

      8. associate-*r* N/A

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

      9. distribute-lft-out-- N/A

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

      10. associate-*r/ N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

   10. Applied rewrites 74.2%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 65.5%

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

   if -5.09999999999999996e151 < z < -1.64999999999999988e33

   1. Initial program 62.5%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 62.9

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

   5. Applied rewrites 62.9%

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

   if -1.64999999999999988e33 < z < 2.9000000000000002e76

   1. Initial program 82.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 90.6

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

   4. Applied rewrites 90.6%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 74.9

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

   7. Applied rewrites 74.9%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+151}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{+33}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+27} \lor \neg \left(z \leq 9.8 \cdot 10^{+33}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{-\left(t - x\right)}{z}, y - a, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.2e+27) (not (<= z 9.8e+33)))
   (fma (/ (- (- t x)) z) (- y a) t)
   (fma (- y z) (/ (- t x) a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.2e+27) || !(z <= 9.8e+33)) {
		tmp = fma((-(t - x) / z), (y - a), t);
	} else {
		tmp = fma((y - z), ((t - x) / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.2e+27) || !(z <= 9.8e+33))
		tmp = fma(Float64(Float64(-Float64(t - x)) / z), Float64(y - a), t);
	else
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.2e+27], N[Not[LessEqual[z, 9.8e+33]], $MachinePrecision]], N[(N[((-N[(t - x), $MachinePrecision]) / z), $MachinePrecision] * N[(y - a), $MachinePrecision] + t), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.20000000000000015e27 or 9.80000000000000027e33 < z

   1. Initial program 40.6%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

      9. distribute-rgt-out-- N/A

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

      10. distribute-lft-neg-in N/A

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 82.0%

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

   if -3.20000000000000015e27 < z < 9.80000000000000027e33

   1. Initial program 85.1%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 80.6

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

   5. Applied rewrites 80.6%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+27} \lor \neg \left(z \leq 9.8 \cdot 10^{+33}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{-\left(t - x\right)}{z}, y - a, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+51}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-297}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(-x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e+51)
   t
   (if (<= z 6.2e-297)
     (fma y (/ t a) x)
     (if (<= z 3.4e+76) (fma (- x) (/ y a) x) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e+51) {
		tmp = t;
	} else if (z <= 6.2e-297) {
		tmp = fma(y, (t / a), x);
	} else if (z <= 3.4e+76) {
		tmp = fma(-x, (y / a), x);
	} else {
		tmp = t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e+51)
		tmp = t;
	elseif (z <= 6.2e-297)
		tmp = fma(y, Float64(t / a), x);
	elseif (z <= 3.4e+76)
		tmp = fma(Float64(-x), Float64(y / a), x);
	else
		tmp = t;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e+51], t, If[LessEqual[z, 6.2e-297], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 3.4e+76], N[((-x) * N[(y / a), $MachinePrecision] + x), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.4999999999999999e51 or 3.3999999999999997e76 < z

   1. Initial program 35.3%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. distribute-lft-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 51.2

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

   5. Applied rewrites 51.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 52.6%

      \[\leadsto \mathsf{fma}\left(0, \color{blue}{x}, 1 \cdot t\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 52.6%

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

   if -9.4999999999999999e51 < z < 6.1999999999999993e-297

   1. Initial program 87.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 92.8

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

   4. Applied rewrites 92.8%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

   7. Applied rewrites 84.8%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 69.9

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

   10. Applied rewrites 69.9%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 57.4%

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

   if 6.1999999999999993e-297 < z < 3.3999999999999997e76

   1. Initial program 78.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 88.6

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

   4. Applied rewrites 88.6%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

   7. Applied rewrites 80.4%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 77.9

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

   10. Applied rewrites 77.9%

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

   11. Taylor expanded in t around 0

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

   13. Applied rewrites 62.6%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+51}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-297}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(-x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -35000000 \lor \neg \left(z \leq 10^{+34}\right):\\ \;\;\;\;t - \frac{t - x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -35000000.0) (not (<= z 1e+34)))
   (- t (* (/ (- t x) z) y))
   (fma (- y z) (/ (- t x) a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -35000000.0) || !(z <= 1e+34)) {
		tmp = t - (((t - x) / z) * y);
	} else {
		tmp = fma((y - z), ((t - x) / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -35000000.0) || !(z <= 1e+34))
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * y));
	else
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -35000000.0], N[Not[LessEqual[z, 1e+34]], $MachinePrecision]], N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5e7 or 9.99999999999999946e33 < z

   1. Initial program 41.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 61.2

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

   4. Applied rewrites 61.2%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

   7. Applied rewrites 77.8%

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

   8. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r* N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. mul-1-neg N/A

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

      8. associate-*r* N/A

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

      9. distribute-lft-out-- N/A

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

      10. associate-*r/ N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

   10. Applied rewrites 68.7%

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

   11. Taylor expanded in a around 0

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

   13. Applied rewrites 74.2%

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

   if -3.5e7 < z < 9.99999999999999946e33

   1. Initial program 84.9%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 81.1

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

   5. Applied rewrites 81.1%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -35000000 \lor \neg \left(z \leq 10^{+34}\right):\\ \;\;\;\;t - \frac{t - x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-10} \lor \neg \left(z \leq 10^{+34}\right):\\ \;\;\;\;t - \frac{t - x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.7e-10) (not (<= z 1e+34)))
   (- t (* (/ (- t x) z) y))
   (fma (- t x) (/ y a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.7e-10) || !(z <= 1e+34)) {
		tmp = t - (((t - x) / z) * y);
	} else {
		tmp = fma((t - x), (y / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.7e-10) || !(z <= 1e+34))
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * y));
	else
		tmp = fma(Float64(t - x), Float64(y / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.7e-10], N[Not[LessEqual[z, 1e+34]], $MachinePrecision]], N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.70000000000000007e-10 or 9.99999999999999946e33 < z

   1. Initial program 42.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 61.9

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

   4. Applied rewrites 61.9%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

   7. Applied rewrites 78.0%

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

   8. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r* N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. mul-1-neg N/A

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

      8. associate-*r* N/A

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

      9. distribute-lft-out-- N/A

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

      10. associate-*r/ N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

   10. Applied rewrites 67.6%

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

   11. Taylor expanded in a around 0

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

   13. Applied rewrites 73.0%

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

   if -1.70000000000000007e-10 < z < 9.99999999999999946e33

   1. Initial program 85.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 91.4

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

   4. Applied rewrites 91.4%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 79.7

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

   7. Applied rewrites 79.7%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-10} \lor \neg \left(z \leq 10^{+34}\right):\\ \;\;\;\;t - \frac{t - x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+51} \lor \neg \left(z \leq 2.9 \cdot 10^{+76}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.5e+51) (not (<= z 2.9e+76)))
   (fma (/ (- t x) z) a t)
   (fma (- t x) (/ y a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+51) || !(z <= 2.9e+76)) {
		tmp = fma(((t - x) / z), a, t);
	} else {
		tmp = fma((t - x), (y / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.5e+51) || !(z <= 2.9e+76))
		tmp = fma(Float64(Float64(t - x) / z), a, t);
	else
		tmp = fma(Float64(t - x), Float64(y / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.5e+51], N[Not[LessEqual[z, 2.9e+76]], $MachinePrecision]], N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * a + t), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.4999999999999999e51 or 2.9000000000000002e76 < z

   1. Initial program 35.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 55.4

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

   4. Applied rewrites 55.4%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

   7. Applied rewrites 76.2%

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

   8. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r* N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. mul-1-neg N/A

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

      8. associate-*r* N/A

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

      9. distribute-lft-out-- N/A

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

      10. associate-*r/ N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

   10. Applied rewrites 70.6%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 60.3%

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

   if -9.4999999999999999e51 < z < 2.9000000000000002e76

   1. Initial program 83.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 90.9

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

   4. Applied rewrites 90.9%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 74.2

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

   7. Applied rewrites 74.2%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+51} \lor \neg \left(z \leq 2.9 \cdot 10^{+76}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+51} \lor \neg \left(z \leq 2.9 \cdot 10^{+76}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.5e+51) (not (<= z 2.9e+76)))
   (fma (/ (- t x) z) a t)
   (fma (/ (- t x) a) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+51) || !(z <= 2.9e+76)) {
		tmp = fma(((t - x) / z), a, t);
	} else {
		tmp = fma(((t - x) / a), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.5e+51) || !(z <= 2.9e+76))
		tmp = fma(Float64(Float64(t - x) / z), a, t);
	else
		tmp = fma(Float64(Float64(t - x) / a), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.5e+51], N[Not[LessEqual[z, 2.9e+76]], $MachinePrecision]], N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * a + t), $MachinePrecision], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.4999999999999999e51 or 2.9000000000000002e76 < z

   1. Initial program 35.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 55.4

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

   4. Applied rewrites 55.4%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

   7. Applied rewrites 76.2%

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

   8. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r* N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. mul-1-neg N/A

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

      8. associate-*r* N/A

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

      9. distribute-lft-out-- N/A

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

      10. associate-*r/ N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

   10. Applied rewrites 70.6%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 60.3%

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

   if -9.4999999999999999e51 < z < 2.9000000000000002e76

   1. Initial program 83.2%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 73.6

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

   5. Applied rewrites 73.6%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+51} \lor \neg \left(z \leq 2.9 \cdot 10^{+76}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+51}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e+51) t (if (<= z 3.8e+76) (fma (/ (- t x) a) y x) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e+51) {
		tmp = t;
	} else if (z <= 3.8e+76) {
		tmp = fma(((t - x) / a), y, x);
	} else {
		tmp = t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e+51)
		tmp = t;
	elseif (z <= 3.8e+76)
		tmp = fma(Float64(Float64(t - x) / a), y, x);
	else
		tmp = t;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e+51], t, If[LessEqual[z, 3.8e+76], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y + x), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -9.4999999999999999e51 or 3.80000000000000024e76 < z

   1. Initial program 35.3%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. distribute-lft-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 51.2

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

   5. Applied rewrites 51.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 52.6%

      \[\leadsto \mathsf{fma}\left(0, \color{blue}{x}, 1 \cdot t\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 52.6%

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

   if -9.4999999999999999e51 < z < 3.80000000000000024e76

   1. Initial program 83.2%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 73.6

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

   5. Applied rewrites 73.6%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+51}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+51} \lor \neg \left(z \leq 3.7 \cdot 10^{+76}\right):\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.5e+51) (not (<= z 3.7e+76))) t (fma y (/ t a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+51) || !(z <= 3.7e+76)) {
		tmp = t;
	} else {
		tmp = fma(y, (t / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.5e+51) || !(z <= 3.7e+76))
		tmp = t;
	else
		tmp = fma(y, Float64(t / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.5e+51], N[Not[LessEqual[z, 3.7e+76]], $MachinePrecision]], t, N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.4999999999999999e51 or 3.6999999999999999e76 < z

   1. Initial program 35.3%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. distribute-lft-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 51.2

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

   5. Applied rewrites 51.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 52.6%

      \[\leadsto \mathsf{fma}\left(0, \color{blue}{x}, 1 \cdot t\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 52.6%

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

   if -9.4999999999999999e51 < z < 3.6999999999999999e76

   1. Initial program 83.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 90.9

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

   4. Applied rewrites 90.9%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

   7. Applied rewrites 82.7%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 73.6

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

   10. Applied rewrites 73.6%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 56.9%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+51} \lor \neg \left(z \leq 3.7 \cdot 10^{+76}\right):\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 39.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+51} \lor \neg \left(z \leq 8.6 \cdot 10^{+74}\right):\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{z}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.2e+51) (not (<= z 8.6e+74))) t (fma x (/ z a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.2e+51) || !(z <= 8.6e+74)) {
		tmp = t;
	} else {
		tmp = fma(x, (z / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.2e+51) || !(z <= 8.6e+74))
		tmp = t;
	else
		tmp = fma(x, Float64(z / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.2e+51], N[Not[LessEqual[z, 8.6e+74]], $MachinePrecision]], t, N[(x * N[(z / a), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.2000000000000002e51 or 8.60000000000000001e74 < z

   1. Initial program 35.3%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. distribute-lft-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 51.2

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

   5. Applied rewrites 51.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 52.6%

      \[\leadsto \mathsf{fma}\left(0, \color{blue}{x}, 1 \cdot t\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 52.6%

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

   if -9.2000000000000002e51 < z < 8.60000000000000001e74

   1. Initial program 83.2%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. distribute-lft-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 42.7

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

   5. Applied rewrites 42.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 35.2%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 36.8%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+51} \lor \neg \left(z \leq 8.6 \cdot 10^{+74}\right):\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{z}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+33} \lor \neg \left(z \leq 1.2 \cdot 10^{+35}\right):\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.1e+33) (not (<= z 1.2e+35))) t (* (/ x t) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.1e+33) || !(z <= 1.2e+35)) {
		tmp = t;
	} else {
		tmp = (x / t) * 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 ((z <= (-4.1d+33)) .or. (.not. (z <= 1.2d+35))) then
        tmp = t
    else
        tmp = (x / t) * 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 ((z <= -4.1e+33) || !(z <= 1.2e+35)) {
		tmp = t;
	} else {
		tmp = (x / t) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.1e+33) or not (z <= 1.2e+35):
		tmp = t
	else:
		tmp = (x / t) * t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.1e+33) || !(z <= 1.2e+35))
		tmp = t;
	else
		tmp = Float64(Float64(x / t) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.1e+33) || ~((z <= 1.2e+35)))
		tmp = t;
	else
		tmp = (x / t) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.1e+33], N[Not[LessEqual[z, 1.2e+35]], $MachinePrecision]], t, N[(N[(x / t), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.09999999999999995e33 or 1.20000000000000007e35 < z

   1. Initial program 40.6%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. distribute-lft-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 50.0

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

   5. Applied rewrites 50.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 48.1%

      \[\leadsto \mathsf{fma}\left(0, \color{blue}{x}, 1 \cdot t\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 48.1%

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

   if -4.09999999999999995e33 < z < 1.20000000000000007e35

   1. Initial program 85.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 91.1

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

   4. Applied rewrites 91.1%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

   7. Applied rewrites 82.5%

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

   8. Taylor expanded in a around inf

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

   10. Applied rewrites 37.7%

       \[\leadsto \frac{x}{t} \cdot t \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+33} \lor \neg \left(z \leq 1.2 \cdot 10^{+35}\right):\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 39.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{-7} \lor \neg \left(a \leq 9.5 \cdot 10^{+48}\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.5e-7) (not (<= a 9.5e+48))) (* 1.0 x) t))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.5e-7) || !(a <= 9.5e+48)) {
		tmp = 1.0 * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.5d-7)) .or. (.not. (a <= 9.5d+48))) then
        tmp = 1.0d0 * x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.5e-7) || !(a <= 9.5e+48)) {
		tmp = 1.0 * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.5e-7) or not (a <= 9.5e+48):
		tmp = 1.0 * x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.5e-7) || !(a <= 9.5e+48))
		tmp = Float64(1.0 * x);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.5e-7) || ~((a <= 9.5e+48)))
		tmp = 1.0 * x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.5e-7], N[Not[LessEqual[a, 9.5e+48]], $MachinePrecision]], N[(1.0 * x), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if a < -3.49999999999999984e-7 or 9.4999999999999997e48 < a

   1. Initial program 70.3%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. distribute-lft-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 62.8

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

   5. Applied rewrites 62.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 49.0%

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

   9. Taylor expanded in z around 0

      \[\leadsto 1 \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 46.8%

       \[\leadsto 1 \cdot x \]

   if -3.49999999999999984e-7 < a < 9.4999999999999997e48

   1. Initial program 58.3%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. distribute-lft-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 33.3

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

   5. Applied rewrites 33.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 38.8%

      \[\leadsto \mathsf{fma}\left(0, \color{blue}{x}, 1 \cdot t\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 38.8%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{-7} \lor \neg \left(a \leq 9.5 \cdot 10^{+48}\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 25.0% accurate, 29.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 63.6%

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

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. mul-1-neg N/A

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

   3. *-commutative N/A

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

   4. associate-/l* N/A

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

   5. distribute-lft-neg-in N/A

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

   6. mul-1-neg N/A

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

   7. lower-fma.f64 N/A

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

   8. mul-1-neg N/A

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

   9. lower-neg.f64 N/A

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

   10. lower--.f64 N/A

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

   11. lower-/.f64 N/A

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

   12. lower--.f64 46.2

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

5. Applied rewrites 46.2%

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

6. Taylor expanded in z around inf

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

8. Applied rewrites 27.0%

   \[\leadsto \mathsf{fma}\left(0, \color{blue}{x}, 1 \cdot t\right) \]
9. Step-by-step derivation

10. Applied rewrites 27.0%

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

11. Final simplification 27.0%

    \[\leadsto t \]
12. Add Preprocessing

Developer Target 1: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - 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 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - 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 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024326 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -125361310560950360000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- t (* (/ y z) (- t x))) (if (< z 44467023691138110000000000000000000000000000000000000000000000000) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x))))))

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