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

Percentage Accurate: 67.9% → 86.8%

Time: 9.0s

Alternatives: 18

Speedup: 0.9×

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: 67.9% 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: 86.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.1 \cdot 10^{+81}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, {z}^{-1} \cdot \left(a - y\right), t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z 2.1e+81)
   (fma (- t x) (/ (- y z) (- a z)) x)
   (fma (- t x) (* (pow z -1.0) (- a y)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 2.1e+81) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = fma((t - x), (pow(z, -1.0) * (a - y)), t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 2.1e+81)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = fma(Float64(t - x), Float64((z ^ -1.0) * Float64(a - y)), t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 2.1e+81], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * N[(N[Power[z, -1.0], $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.0999999999999999e81

   1. Initial program 79.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 89.9

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

   4. Applied rewrites 89.9%

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

   if 2.0999999999999999e81 < z

   1. Initial program 27.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. div-sub N/A

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

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

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

      7. associate-/l* N/A

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

      8. associate-*r* N/A

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

      9. mul-1-neg N/A

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

      10. associate-/l* N/A

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

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

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

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

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

      13. lower-fma.f64 N/A

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

   5. Applied rewrites 87.4%

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

   7. Applied rewrites 91.4%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.1 \cdot 10^{+81}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, {z}^{-1} \cdot \left(a - y\right), t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 66.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-8}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+17}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+125}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- t x) z) a t)))
   (if (<= z -1.15e+149)
     t_1
     (if (<= z -4.2e-8)
       (* (- y z) (/ t (- a z)))
       (if (<= z 5.4e+17)
         (fma (- t x) (/ y a) x)
         (if (<= z 7.2e+125) (/ (* (- y z) t) (- a z)) 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 <= -1.15e+149) {
		tmp = t_1;
	} else if (z <= -4.2e-8) {
		tmp = (y - z) * (t / (a - z));
	} else if (z <= 5.4e+17) {
		tmp = fma((t - x), (y / a), x);
	} else if (z <= 7.2e+125) {
		tmp = ((y - z) * t) / (a - z);
	} 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 <= -1.15e+149)
		tmp = t_1;
	elseif (z <= -4.2e-8)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	elseif (z <= 5.4e+17)
		tmp = fma(Float64(t - x), Float64(y / a), x);
	elseif (z <= 7.2e+125)
		tmp = Float64(Float64(Float64(y - z) * t) / Float64(a - z));
	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, -1.15e+149], t$95$1, If[LessEqual[z, -4.2e-8], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+17], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 7.2e+125], N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1499999999999999e149 or 7.2000000000000007e125 < z

   1. Initial program 29.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. div-sub N/A

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

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

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

      7. associate-/l* N/A

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

      8. associate-*r* N/A

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

      9. mul-1-neg N/A

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

      10. associate-/l* N/A

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

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

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

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

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

      13. lower-fma.f64 N/A

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

   5. Applied rewrites 85.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 73.4%

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

   if -1.1499999999999999e149 < z < -4.19999999999999989e-8

   1. Initial program 60.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 63.5

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

   5. Applied rewrites 63.5%

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

   if -4.19999999999999989e-8 < z < 5.4e17

   1. Initial program 92.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 95.4

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

   4. Applied rewrites 95.4%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 41.2

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

   7. Applied rewrites 41.2%

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

   8. Taylor expanded in a around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 83.7

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

   10. Applied rewrites 83.7%

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

   11. Taylor expanded in y around inf

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

   13. Applied rewrites 79.9%

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

   if 5.4e17 < z < 7.2000000000000007e125

   1. Initial program 73.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 86.8

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

   4. Applied rewrites 86.8%

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

   5. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 61.7

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

   7. Applied rewrites 61.7%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+149}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-8}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+17}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+125}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ t_2 := \mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+149}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+17}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ t (- a z)))) (t_2 (fma (/ (- t x) z) a t)))
   (if (<= z -1.15e+149)
     t_2
     (if (<= z -4.2e-8)
       t_1
       (if (<= z 5.4e+17)
         (fma (- t x) (/ y a) x)
         (if (<= z 9.6e+125) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / (a - z));
	double t_2 = fma(((t - x) / z), a, t);
	double tmp;
	if (z <= -1.15e+149) {
		tmp = t_2;
	} else if (z <= -4.2e-8) {
		tmp = t_1;
	} else if (z <= 5.4e+17) {
		tmp = fma((t - x), (y / a), x);
	} else if (z <= 9.6e+125) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * Float64(t / Float64(a - z)))
	t_2 = fma(Float64(Float64(t - x) / z), a, t)
	tmp = 0.0
	if (z <= -1.15e+149)
		tmp = t_2;
	elseif (z <= -4.2e-8)
		tmp = t_1;
	elseif (z <= 5.4e+17)
		tmp = fma(Float64(t - x), Float64(y / a), x);
	elseif (z <= 9.6e+125)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * a + t), $MachinePrecision]}, If[LessEqual[z, -1.15e+149], t$95$2, If[LessEqual[z, -4.2e-8], t$95$1, If[LessEqual[z, 5.4e+17], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 9.6e+125], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1499999999999999e149 or 9.5999999999999999e125 < z

   1. Initial program 29.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. div-sub N/A

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

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

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

      7. associate-/l* N/A

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

      8. associate-*r* N/A

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

      9. mul-1-neg N/A

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

      10. associate-/l* N/A

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

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

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

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

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

      13. lower-fma.f64 N/A

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

   5. Applied rewrites 85.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 73.4%

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

   if -1.1499999999999999e149 < z < -4.19999999999999989e-8 or 5.4e17 < z < 9.5999999999999999e125

   1. Initial program 65.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 62.6

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

   5. Applied rewrites 62.6%

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

   if -4.19999999999999989e-8 < z < 5.4e17

   1. Initial program 92.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 95.4

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

   4. Applied rewrites 95.4%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 41.2

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

   7. Applied rewrites 41.2%

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

   8. Taylor expanded in a around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 83.7

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

   10. Applied rewrites 83.7%

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

   11. Taylor expanded in y around inf

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

   13. Applied rewrites 79.9%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+149}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-8}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+17}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+125}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-144}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+79}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ (- t x) z) (- y a)))))
   (if (<= z -4.6e+41)
     t_1
     (if (<= z 2.4e-144)
       (fma (- t x) (/ (- y z) a) x)
       (if (<= z 3.2e+79) (+ x (/ (* (- y z) t) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (((t - x) / z) * (y - a));
	double tmp;
	if (z <= -4.6e+41) {
		tmp = t_1;
	} else if (z <= 2.4e-144) {
		tmp = fma((t - x), ((y - z) / a), x);
	} else if (z <= 3.2e+79) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)))
	tmp = 0.0
	if (z <= -4.6e+41)
		tmp = t_1;
	elseif (z <= 2.4e-144)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / a), x);
	elseif (z <= 3.2e+79)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e+41], t$95$1, If[LessEqual[z, 2.4e-144], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 3.2e+79], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5999999999999997e41 or 3.20000000000000003e79 < z

   1. Initial program 38.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 67.9

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

   4. Applied rewrites 67.9%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. 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. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. lower--.f64 N/A

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

      7. div-sub N/A

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

      8. associate-/l* N/A

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

      9. associate-/l* N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 81.4

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

   7. Applied rewrites 81.4%

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

   if -4.5999999999999997e41 < z < 2.39999999999999994e-144

   1. Initial program 91.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 95.6

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

   4. Applied rewrites 95.6%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 86.6

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

   7. Applied rewrites 86.6%

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

   if 2.39999999999999994e-144 < z < 3.20000000000000003e79

   1. Initial program 89.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 79.1

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

   5. Applied rewrites 79.1%

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

Alternative 5: 76.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+41} \lor \neg \left(z \leq 1.8 \cdot 10^{+25}\right):\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.6e+41) (not (<= z 1.8e+25)))
   (- t (* (/ (- t x) z) (- y a)))
   (fma (- t x) (/ (- y z) a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.6e+41) || !(z <= 1.8e+25)) {
		tmp = t - (((t - x) / z) * (y - a));
	} else {
		tmp = fma((t - x), ((y - z) / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.6e+41) || !(z <= 1.8e+25))
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)));
	else
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.6e+41], N[Not[LessEqual[z, 1.8e+25]], $MachinePrecision]], N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5999999999999997e41 or 1.80000000000000008e25 < z

   1. Initial program 42.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 70.5

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

   4. Applied rewrites 70.5%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. 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. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. lower--.f64 N/A

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

      7. div-sub N/A

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

      8. associate-/l* N/A

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

      9. associate-/l* N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 78.9

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

   7. Applied rewrites 78.9%

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

   if -4.5999999999999997e41 < z < 1.80000000000000008e25

   1. Initial program 92.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 95.6

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

   4. Applied rewrites 95.6%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 82.9

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

   7. Applied rewrites 82.9%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+41} \lor \neg \left(z \leq 1.8 \cdot 10^{+25}\right):\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+66}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a - y}{z}, t, t\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+120}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e+66)
   (fma (/ (- a y) z) t t)
   (if (<= z 2.35e+120)
     (fma (- t x) (/ (- y z) a) x)
     (fma (/ (- t x) z) a t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e+66) {
		tmp = fma(((a - y) / z), t, t);
	} else if (z <= 2.35e+120) {
		tmp = fma((t - x), ((y - z) / a), x);
	} else {
		tmp = fma(((t - x) / z), a, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e+66)
		tmp = fma(Float64(Float64(a - y) / z), t, t);
	elseif (z <= 2.35e+120)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / a), x);
	else
		tmp = fma(Float64(Float64(t - x) / z), a, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e+66], N[(N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision] * t + t), $MachinePrecision], If[LessEqual[z, 2.35e+120], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * a + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.49999999999999996e66

   1. Initial program 48.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. div-sub N/A

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

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

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

      7. associate-/l* N/A

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

      8. associate-*r* N/A

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

      9. mul-1-neg N/A

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

      10. associate-/l* N/A

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

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

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

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

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

      13. lower-fma.f64 N/A

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

   5. Applied rewrites 77.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 65.1%

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

   if -2.49999999999999996e66 < z < 2.34999999999999997e120

   1. Initial program 88.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 93.9

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

   4. Applied rewrites 93.9%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 78.3

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

   7. Applied rewrites 78.3%

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

   if 2.34999999999999997e120 < z

   1. Initial program 22.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. div-sub N/A

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

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

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

      7. associate-/l* N/A

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

      8. associate-*r* N/A

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

      9. mul-1-neg N/A

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

      10. associate-/l* N/A

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

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

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

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

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

      13. lower-fma.f64 N/A

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

   5. Applied rewrites 87.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 70.4%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+66}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a - y}{z}, t, t\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+120}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a - y}{z}, t, t\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+119}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9e+65)
   (fma (/ (- a y) z) t t)
   (if (<= z 4.9e+119) (fma (- y z) (/ (- t x) a) x) (fma (/ (- t x) z) a t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9e+65) {
		tmp = fma(((a - y) / z), t, t);
	} else if (z <= 4.9e+119) {
		tmp = fma((y - z), ((t - x) / a), x);
	} else {
		tmp = fma(((t - x) / z), a, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9e+65)
		tmp = fma(Float64(Float64(a - y) / z), t, t);
	elseif (z <= 4.9e+119)
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / a), x);
	else
		tmp = fma(Float64(Float64(t - x) / z), a, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9e+65], N[(N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision] * t + t), $MachinePrecision], If[LessEqual[z, 4.9e+119], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * a + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9e65

   1. Initial program 48.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. div-sub N/A

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

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

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

      7. associate-/l* N/A

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

      8. associate-*r* N/A

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

      9. mul-1-neg N/A

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

      10. associate-/l* N/A

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

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

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

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

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

      13. lower-fma.f64 N/A

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

   5. Applied rewrites 77.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 65.1%

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

   if -9e65 < z < 4.89999999999999996e119

   1. Initial program 88.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 75.7

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

   5. Applied rewrites 75.7%

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

   if 4.89999999999999996e119 < z

   1. Initial program 22.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. div-sub N/A

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

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

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

      7. associate-/l* N/A

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

      8. associate-*r* N/A

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

      9. mul-1-neg N/A

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

      10. associate-/l* N/A

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

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

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

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

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

      13. lower-fma.f64 N/A

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

   5. Applied rewrites 87.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 70.4%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a - y}{z}, t, t\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+119}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+43} \lor \neg \left(z \leq 3.5 \cdot 10^{+28}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{a - y}{z}, t, t\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.5e+43) (not (<= z 3.5e+28)))
   (fma (/ (- a y) z) t t)
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.5e+43) || !(z <= 3.5e+28)) {
		tmp = fma(((a - y) / z), t, t);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.5e+43) || !(z <= 3.5e+28))
		tmp = fma(Float64(Float64(a - y) / z), t, t);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.5e+43], N[Not[LessEqual[z, 3.5e+28]], $MachinePrecision]], N[(N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision] * t + t), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.50000000000000008e43 or 3.5e28 < z

   1. Initial program 42.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. div-sub N/A

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

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

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

      7. associate-/l* N/A

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

      8. associate-*r* N/A

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

      9. mul-1-neg N/A

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

      10. associate-/l* N/A

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

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

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

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

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

      13. lower-fma.f64 N/A

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

   5. Applied rewrites 78.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 58.6%

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

   if -1.50000000000000008e43 < z < 3.5e28

   1. Initial program 92.1%

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

   3. Taylor expanded in a around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 82.9

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

   5. Applied rewrites 82.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 66.8%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 64.5%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+43} \lor \neg \left(z \leq 3.5 \cdot 10^{+28}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{a - y}{z}, t, t\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a - y}{z}, t, t\right)\\ \mathbf{elif}\;z \leq 1.78 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.5e+43)
   (fma (/ (- a y) z) t t)
   (if (<= z 1.78e+112) (fma (- t x) (/ y a) x) (fma (/ (- t x) z) a t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+43) {
		tmp = fma(((a - y) / z), t, t);
	} else if (z <= 1.78e+112) {
		tmp = fma((t - x), (y / a), x);
	} else {
		tmp = fma(((t - x) / z), a, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.5e+43)
		tmp = fma(Float64(Float64(a - y) / z), t, t);
	elseif (z <= 1.78e+112)
		tmp = fma(Float64(t - x), Float64(y / a), x);
	else
		tmp = fma(Float64(Float64(t - x) / z), a, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.5e+43], N[(N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision] * t + t), $MachinePrecision], If[LessEqual[z, 1.78e+112], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * a + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.50000000000000008e43

   1. Initial program 46.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. div-sub N/A

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

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

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

      7. associate-/l* N/A

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

      8. associate-*r* N/A

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

      9. mul-1-neg N/A

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

      10. associate-/l* N/A

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

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

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

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

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

      13. lower-fma.f64 N/A

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

   5. Applied rewrites 76.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 60.2%

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

   if -1.50000000000000008e43 < z < 1.78e112

   1. Initial program 90.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 94.9

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

   4. Applied rewrites 94.9%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 43.3

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

   7. Applied rewrites 43.3%

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

   8. Taylor expanded in a around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 79.3

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

   10. Applied rewrites 79.3%

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

   11. Taylor expanded in y around inf

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

   13. Applied rewrites 72.8%

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

   if 1.78e112 < z

   1. Initial program 22.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. div-sub N/A

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

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

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

      7. associate-/l* N/A

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

      8. associate-*r* N/A

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

      9. mul-1-neg N/A

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

      10. associate-/l* N/A

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

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

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

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

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

      13. lower-fma.f64 N/A

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

   5. Applied rewrites 87.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 70.4%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a - y}{z}, t, t\right)\\ \mathbf{elif}\;z \leq 1.78 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a - y}{z}, t, t\right)\\ \mathbf{elif}\;z \leq 1.78 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.5e+43)
   (fma (/ (- a y) z) t t)
   (if (<= z 1.78e+112) (fma (/ (- t x) a) y x) (fma (/ (- t x) z) a t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+43) {
		tmp = fma(((a - y) / z), t, t);
	} else if (z <= 1.78e+112) {
		tmp = fma(((t - x) / a), y, x);
	} else {
		tmp = fma(((t - x) / z), a, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.5e+43)
		tmp = fma(Float64(Float64(a - y) / z), t, t);
	elseif (z <= 1.78e+112)
		tmp = fma(Float64(Float64(t - x) / a), y, x);
	else
		tmp = fma(Float64(Float64(t - x) / z), a, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.5e+43], N[(N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision] * t + t), $MachinePrecision], If[LessEqual[z, 1.78e+112], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * a + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.50000000000000008e43

   1. Initial program 46.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. div-sub N/A

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

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

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

      7. associate-/l* N/A

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

      8. associate-*r* N/A

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

      9. mul-1-neg N/A

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

      10. associate-/l* N/A

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

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

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

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

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

      13. lower-fma.f64 N/A

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

   5. Applied rewrites 76.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 60.2%

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

   if -1.50000000000000008e43 < z < 1.78e112

   1. Initial program 90.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 70.2

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

   5. Applied rewrites 70.2%

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

   if 1.78e112 < z

   1. Initial program 22.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. div-sub N/A

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

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

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

      7. associate-/l* N/A

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

      8. associate-*r* N/A

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

      9. mul-1-neg N/A

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

      10. associate-/l* N/A

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

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

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

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

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

      13. lower-fma.f64 N/A

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

   5. Applied rewrites 87.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 70.4%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a - y}{z}, t, t\right)\\ \mathbf{elif}\;z \leq 1.78 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a - y}{z}, t, t\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+28}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.5e+43)
   (fma (/ (- a y) z) t t)
   (if (<= z 6.6e+28) (+ x (* t (/ y a))) (fma (/ (- t x) z) a t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+43) {
		tmp = fma(((a - y) / z), t, t);
	} else if (z <= 6.6e+28) {
		tmp = x + (t * (y / a));
	} else {
		tmp = fma(((t - x) / z), a, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.5e+43)
		tmp = fma(Float64(Float64(a - y) / z), t, t);
	elseif (z <= 6.6e+28)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = fma(Float64(Float64(t - x) / z), a, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.5e+43], N[(N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision] * t + t), $MachinePrecision], If[LessEqual[z, 6.6e+28], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * a + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.50000000000000008e43

   1. Initial program 46.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. div-sub N/A

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

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

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

      7. associate-/l* N/A

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

      8. associate-*r* N/A

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

      9. mul-1-neg N/A

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

      10. associate-/l* N/A

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

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

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

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

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

      13. lower-fma.f64 N/A

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

   5. Applied rewrites 76.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 60.2%

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

   if -1.50000000000000008e43 < z < 6.6e28

   1. Initial program 92.1%

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

   3. Taylor expanded in a around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 82.9

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

   5. Applied rewrites 82.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 66.8%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 64.5%

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

   if 6.6e28 < z

   1. Initial program 37.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. div-sub N/A

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

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

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

      7. associate-/l* N/A

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

      8. associate-*r* N/A

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

      9. mul-1-neg N/A

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

      10. associate-/l* N/A

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

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

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

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

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

      13. lower-fma.f64 N/A

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

   5. Applied rewrites 81.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 57.9%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a - y}{z}, t, t\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+28}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{z}, a, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 86.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3.7 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z 3.7e+84)
   (fma (- t x) (/ (- y z) (- a z)) x)
   (- t (* (/ (- t x) z) (- y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 3.7e+84) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = t - (((t - x) / z) * (y - a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 3.7e+84)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 3.7e+84], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.7e84

   1. Initial program 79.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 89.9

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

   4. Applied rewrites 89.9%

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

   if 3.7e84 < z

   1. Initial program 27.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 61.3

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

   4. Applied rewrites 61.3%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. 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. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. lower--.f64 N/A

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

      7. div-sub N/A

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

      8. associate-/l* N/A

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

      9. associate-/l* N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 87.4

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

   7. Applied rewrites 87.4%

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

Alternative 13: 47.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+180} \lor \neg \left(z \leq 1.85 \cdot 10^{+20}\right):\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.6e+180) (not (<= z 1.85e+20)))
   (+ x (- t x))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.6e+180) || !(z <= 1.85e+20)) {
		tmp = x + (t - x);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.6d+180)) .or. (.not. (z <= 1.85d+20))) then
        tmp = x + (t - x)
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.6e+180) || !(z <= 1.85e+20)) {
		tmp = x + (t - x);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.6e+180) or not (z <= 1.85e+20):
		tmp = x + (t - x)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.6e+180) || !(z <= 1.85e+20))
		tmp = Float64(x + Float64(t - x));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.6e+180) || ~((z <= 1.85e+20)))
		tmp = x + (t - x);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.6e+180], N[Not[LessEqual[z, 1.85e+20]], $MachinePrecision]], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6000000000000002e180 or 1.85e20 < z

   1. Initial program 38.1%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 39.4

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

   5. Applied rewrites 39.4%

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

   if -3.6000000000000002e180 < z < 1.85e20

   1. Initial program 86.0%

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

   3. Taylor expanded in a around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 76.4

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

   5. Applied rewrites 76.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 61.2%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 59.1%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+180} \lor \neg \left(z \leq 1.85 \cdot 10^{+20}\right):\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 31.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-45} \lor \neg \left(y \leq 2.25 \cdot 10^{-113}\right):\\ \;\;\;\;\frac{y}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5e-45) (not (<= y 2.25e-113)))
   (* (/ y (- a z)) t)
   (+ x (- t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5e-45) || !(y <= 2.25e-113)) {
		tmp = (y / (a - z)) * t;
	} else {
		tmp = x + (t - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-5d-45)) .or. (.not. (y <= 2.25d-113))) then
        tmp = (y / (a - z)) * t
    else
        tmp = x + (t - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5e-45) || !(y <= 2.25e-113)) {
		tmp = (y / (a - z)) * t;
	} else {
		tmp = x + (t - x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5e-45) or not (y <= 2.25e-113):
		tmp = (y / (a - z)) * t
	else:
		tmp = x + (t - x)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5e-45) || !(y <= 2.25e-113))
		tmp = Float64(Float64(y / Float64(a - z)) * t);
	else
		tmp = Float64(x + Float64(t - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -5e-45) || ~((y <= 2.25e-113)))
		tmp = (y / (a - z)) * t;
	else
		tmp = x + (t - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5e-45], N[Not[LessEqual[y, 2.25e-113]], $MachinePrecision]], N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.99999999999999976e-45 or 2.2500000000000001e-113 < y

   1. Initial program 75.9%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 69.7

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

   5. Applied rewrites 69.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 47.4%

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

   if -4.99999999999999976e-45 < y < 2.2500000000000001e-113

   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 z around inf

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

      1. lower--.f64 30.5

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

   5. Applied rewrites 30.5%

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

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-45} \lor \neg \left(y \leq 2.25 \cdot 10^{-113}\right):\\ \;\;\;\;\frac{y}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{-45} \lor \neg \left(y \leq 1.95 \cdot 10^{-113}\right):\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5.1e-45) (not (<= y 1.95e-113)))
   (* y (/ t (- a z)))
   (+ x (- t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.1e-45) || !(y <= 1.95e-113)) {
		tmp = y * (t / (a - z));
	} else {
		tmp = x + (t - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-5.1d-45)) .or. (.not. (y <= 1.95d-113))) then
        tmp = y * (t / (a - z))
    else
        tmp = x + (t - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.1e-45) || !(y <= 1.95e-113)) {
		tmp = y * (t / (a - z));
	} else {
		tmp = x + (t - x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5.1e-45) or not (y <= 1.95e-113):
		tmp = y * (t / (a - z))
	else:
		tmp = x + (t - x)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5.1e-45) || !(y <= 1.95e-113))
		tmp = Float64(y * Float64(t / Float64(a - z)));
	else
		tmp = Float64(x + Float64(t - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -5.1e-45) || ~((y <= 1.95e-113)))
		tmp = y * (t / (a - z));
	else
		tmp = x + (t - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5.1e-45], N[Not[LessEqual[y, 1.95e-113]], $MachinePrecision]], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.0999999999999997e-45 or 1.9499999999999999e-113 < y

   1. Initial program 75.9%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 69.7

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

   5. Applied rewrites 69.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 47.4%

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

   10. Applied rewrites 45.7%

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

   if -5.0999999999999997e-45 < y < 1.9499999999999999e-113

   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 z around inf

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

      1. lower--.f64 30.5

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

   5. Applied rewrites 30.5%

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

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{-45} \lor \neg \left(y \leq 1.95 \cdot 10^{-113}\right):\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 24.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-40} \lor \neg \left(y \leq 3.25 \cdot 10^{+122}\right):\\ \;\;\;\;\frac{-y}{z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.55e-40) (not (<= y 3.25e+122)))
   (* (/ (- y) z) t)
   (+ x (- t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.55e-40) || !(y <= 3.25e+122)) {
		tmp = (-y / z) * t;
	} else {
		tmp = x + (t - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.55d-40)) .or. (.not. (y <= 3.25d+122))) then
        tmp = (-y / z) * t
    else
        tmp = x + (t - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.55e-40) || !(y <= 3.25e+122)) {
		tmp = (-y / z) * t;
	} else {
		tmp = x + (t - x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.55e-40) or not (y <= 3.25e+122):
		tmp = (-y / z) * t
	else:
		tmp = x + (t - x)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.55e-40) || !(y <= 3.25e+122))
		tmp = Float64(Float64(Float64(-y) / z) * t);
	else
		tmp = Float64(x + Float64(t - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.55e-40) || ~((y <= 3.25e+122)))
		tmp = (-y / z) * t;
	else
		tmp = x + (t - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.55e-40], N[Not[LessEqual[y, 3.25e+122]], $MachinePrecision]], N[(N[((-y) / z), $MachinePrecision] * t), $MachinePrecision], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.55000000000000005e-40 or 3.24999999999999982e122 < y

   1. Initial program 78.3%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 79.4

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

   5. Applied rewrites 79.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 55.1%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 39.1%

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

   if -1.55000000000000005e-40 < y < 3.24999999999999982e122

   1. Initial program 65.5%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 25.2

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

   5. Applied rewrites 25.2%

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

4. Final simplification 31.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-40} \lor \neg \left(y \leq 3.25 \cdot 10^{+122}\right):\\ \;\;\;\;\frac{-y}{z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 19.9% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ x + \left(t - x\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 70.9%

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

3. Taylor expanded in z around inf

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

   1. lower--.f64 18.3

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

5. Applied rewrites 18.3%

   \[\leadsto x + \color{blue}{\left(t - x\right)} \]
6. Add Preprocessing

Alternative 18: 2.8% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ x + \left(-x\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + (-x)), $MachinePrecision]

Derivation

1. Initial program 70.9%

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

3. Taylor expanded in z around inf

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

   1. lower--.f64 18.3

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

5. Applied rewrites 18.3%

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

6. Taylor expanded in x around inf

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

8. Applied rewrites 2.8%

   \[\leadsto x + \left(-x\right) \]
9. Add Preprocessing

Developer Target 1: 84.1% 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 2024318 
(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))))