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

Percentage Accurate: 67.1% → 88.8%

Time: 11.6s

Alternatives: 16

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: 67.1% 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: 88.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+103}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+136}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{y - a}{z}, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.3e+103)
   (+ t (* (- y a) (/ (- x t) z)))
   (if (<= z 1.45e+136)
     (fma (- t x) (/ (- y z) (- a z)) x)
     (fma (- x t) (/ (- y a) z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e+103) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else if (z <= 1.45e+136) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = fma((x - t), ((y - a) / z), t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.3e+103)
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(x - t) / z)));
	elseif (z <= 1.45e+136)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = fma(Float64(x - t), Float64(Float64(y - a) / z), t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.3e+103], N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+136], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(x - t), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.30000000000000009e103

   1. Initial program 28.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 63.9

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

   4. Applied rewrites 63.9%

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

   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 90.2

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

   7. Applied rewrites 90.2%

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

   if -3.30000000000000009e103 < z < 1.44999999999999987e136

   1. Initial program 88.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 92.8

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

   4. Applied rewrites 92.8%

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

   if 1.44999999999999987e136 < z

   1. Initial program 28.1%

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

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 85.0%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+103}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+136}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{y - a}{z}, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+102}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{-117}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+135}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{y - a}{z}, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.5e+102)
   (+ t (* (- y a) (/ (- x t) z)))
   (if (<= z -6.3e-117)
     (+ x (/ (* t (- y z)) (- a z)))
     (if (<= z 1.42e+135)
       (fma (- y z) (/ (- t x) a) x)
       (fma (- x t) (/ (- y a) z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+102) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else if (z <= -6.3e-117) {
		tmp = x + ((t * (y - z)) / (a - z));
	} else if (z <= 1.42e+135) {
		tmp = fma((y - z), ((t - x) / a), x);
	} else {
		tmp = fma((x - t), ((y - a) / z), t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.5e+102)
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(x - t) / z)));
	elseif (z <= -6.3e-117)
		tmp = Float64(x + Float64(Float64(t * Float64(y - z)) / Float64(a - z)));
	elseif (z <= 1.42e+135)
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / a), x);
	else
		tmp = fma(Float64(x - t), Float64(Float64(y - a) / z), t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.5e+102], N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.3e-117], N[(x + N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.42e+135], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(N[(x - t), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.4999999999999999e102

   1. Initial program 28.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 63.9

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

   4. Applied rewrites 63.9%

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

   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 90.2

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

   7. Applied rewrites 90.2%

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

   if -1.4999999999999999e102 < z < -6.2999999999999997e-117

   1. Initial program 82.7%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 74.2

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

   5. Applied rewrites 74.2%

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

   if -6.2999999999999997e-117 < z < 1.41999999999999998e135

   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 a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 81.6

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

   5. Applied rewrites 81.6%

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

   if 1.41999999999999998e135 < z

   1. Initial program 28.1%

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

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 85.0%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+102}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{-117}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+135}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{y - a}{z}, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+84}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+135}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{y - a}{z}, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.7e+84)
   (+ t (* (- y a) (/ (- x t) z)))
   (if (<= z 1.42e+135)
     (fma (- y z) (/ (- t x) a) x)
     (fma (- x t) (/ (- y a) z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.7e+84) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else if (z <= 1.42e+135) {
		tmp = fma((y - z), ((t - x) / a), x);
	} else {
		tmp = fma((x - t), ((y - a) / z), t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.7e+84)
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(x - t) / z)));
	elseif (z <= 1.42e+135)
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / a), x);
	else
		tmp = fma(Float64(x - t), Float64(Float64(y - a) / z), t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.7e+84], N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.42e+135], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(N[(x - t), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6999999999999999e84

   1. Initial program 28.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 62.8

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

   4. Applied rewrites 62.8%

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

   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 86.6

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

   7. Applied rewrites 86.6%

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

   if -1.6999999999999999e84 < z < 1.41999999999999998e135

   1. Initial program 89.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 77.3

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

   5. Applied rewrites 77.3%

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

   if 1.41999999999999998e135 < z

   1. Initial program 28.1%

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

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 85.0%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+84}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+135}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{y - a}{z}, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x - t, \frac{y - a}{z}, t\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+135}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- x t) (/ (- y a) z) t)))
   (if (<= z -8e+99)
     t_1
     (if (<= z 1.42e+135) (fma (- y z) (/ (- t x) a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x - t), ((y - a) / z), t);
	double tmp;
	if (z <= -8e+99) {
		tmp = t_1;
	} else if (z <= 1.42e+135) {
		tmp = fma((y - z), ((t - x) / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x - t), Float64(Float64(y - a) / z), t)
	tmp = 0.0
	if (z <= -8e+99)
		tmp = t_1;
	elseif (z <= 1.42e+135)
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - t), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[z, -8e+99], t$95$1, If[LessEqual[z, 1.42e+135], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.9999999999999997e99 or 1.41999999999999998e135 < z

   1. Initial program 28.3%

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

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 86.4%

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

   if -7.9999999999999997e99 < z < 1.41999999999999998e135

   1. Initial program 88.4%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 76.7

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

   5. Applied rewrites 76.7%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{y - a}{z}, t\right)\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+135}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{y - a}{z}, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{x - t}{z}, t\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+135}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ (- x t) z) t)))
   (if (<= z -8e+99)
     t_1
     (if (<= z 1.42e+135) (fma (- y z) (/ (- t x) a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, ((x - t) / z), t);
	double tmp;
	if (z <= -8e+99) {
		tmp = t_1;
	} else if (z <= 1.42e+135) {
		tmp = fma((y - z), ((t - x) / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(Float64(x - t) / z), t)
	tmp = 0.0
	if (z <= -8e+99)
		tmp = t_1;
	elseif (z <= 1.42e+135)
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[z, -8e+99], t$95$1, If[LessEqual[z, 1.42e+135], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.9999999999999997e99 or 1.41999999999999998e135 < z

   1. Initial program 28.3%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. mul-1-neg N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 44.6

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

   5. Applied rewrites 44.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 10.3%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 77.0%

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

   if -7.9999999999999997e99 < z < 1.41999999999999998e135

   1. Initial program 88.4%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 76.7

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

   5. Applied rewrites 76.7%

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

Alternative 6: 68.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{x - t}{z}, t\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+28}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ (- x t) z) t)))
   (if (<= z -8e+99) t_1 (if (<= z 2.2e+28) (fma (- t x) (/ y a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, ((x - t) / z), t);
	double tmp;
	if (z <= -8e+99) {
		tmp = t_1;
	} else if (z <= 2.2e+28) {
		tmp = fma((t - x), (y / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(Float64(x - t) / z), t)
	tmp = 0.0
	if (z <= -8e+99)
		tmp = t_1;
	elseif (z <= 2.2e+28)
		tmp = fma(Float64(t - x), Float64(y / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[z, -8e+99], t$95$1, If[LessEqual[z, 2.2e+28], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.9999999999999997e99 or 2.19999999999999986e28 < z

   1. Initial program 37.2%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. mul-1-neg N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 43.5

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

   5. Applied rewrites 43.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 10.4%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 71.3%

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

   if -7.9999999999999997e99 < z < 2.19999999999999986e28

   1. Initial program 89.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 92.9

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

   4. Applied rewrites 92.9%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 72.7

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

   7. Applied rewrites 72.7%

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

Alternative 7: 67.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{x - t}{z}, t\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+28}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ (- x t) z) t)))
   (if (<= z -8e+99) t_1 (if (<= z 2.2e+28) (fma y (/ (- t x) a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, ((x - t) / z), t);
	double tmp;
	if (z <= -8e+99) {
		tmp = t_1;
	} else if (z <= 2.2e+28) {
		tmp = fma(y, ((t - x) / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(Float64(x - t) / z), t)
	tmp = 0.0
	if (z <= -8e+99)
		tmp = t_1;
	elseif (z <= 2.2e+28)
		tmp = fma(y, Float64(Float64(t - x) / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[z, -8e+99], t$95$1, If[LessEqual[z, 2.2e+28], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.9999999999999997e99 or 2.19999999999999986e28 < z

   1. Initial program 37.2%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. mul-1-neg N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 43.5

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

   5. Applied rewrites 43.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 10.4%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 71.3%

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

   if -7.9999999999999997e99 < z < 2.19999999999999986e28

   1. Initial program 89.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 72.0

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

   5. Applied rewrites 72.0%

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

Alternative 8: 62.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, \frac{x - t}{a}, x\right)\\ \mathbf{if}\;a \leq -2.9 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.35 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{x - t}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma z (/ (- x t) a) x)))
   (if (<= a -2.9e+69) t_1 (if (<= a 4.35e+99) (fma y (/ (- x t) z) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(z, ((x - t) / a), x);
	double tmp;
	if (a <= -2.9e+69) {
		tmp = t_1;
	} else if (a <= 4.35e+99) {
		tmp = fma(y, ((x - t) / z), t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(z, Float64(Float64(x - t) / a), x)
	tmp = 0.0
	if (a <= -2.9e+69)
		tmp = t_1;
	elseif (a <= 4.35e+99)
		tmp = fma(y, Float64(Float64(x - t) / z), t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -2.9e+69], t$95$1, If[LessEqual[a, 4.35e+99], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.8999999999999998e69 or 4.3499999999999998e99 < a

   1. Initial program 74.1%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lower-/.f64 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. remove-double-neg N/A

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

      14. lower-+.f64 N/A

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

      15. lower-neg.f64 72.7

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

   5. Applied rewrites 72.7%

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

   7. Applied rewrites 61.2%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 69.5%

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

   if -2.8999999999999998e69 < a < 4.3499999999999998e99

   1. Initial program 67.5%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. mul-1-neg N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 45.0

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

   5. Applied rewrites 45.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 17.1%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 61.1%

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

Alternative 9: 61.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-x, \frac{y}{a}, x\right)\\ \mathbf{if}\;a \leq -2.55 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 0.00025:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{x - t}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- x) (/ y a) x)))
   (if (<= a -2.55e+69) t_1 (if (<= a 0.00025) (fma y (/ (- x t) z) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(-x, (y / a), x);
	double tmp;
	if (a <= -2.55e+69) {
		tmp = t_1;
	} else if (a <= 0.00025) {
		tmp = fma(y, ((x - t) / z), t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(-x), Float64(y / a), x)
	tmp = 0.0
	if (a <= -2.55e+69)
		tmp = t_1;
	elseif (a <= 0.00025)
		tmp = fma(y, Float64(Float64(x - t) / z), t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-x) * N[(y / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -2.55e+69], t$95$1, If[LessEqual[a, 0.00025], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.54999999999999999e69 or 2.5000000000000001e-4 < a

   1. Initial program 71.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 90.5

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

   4. Applied rewrites 90.5%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 69.7

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

   7. Applied rewrites 69.7%

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

   8. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 55.8

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

   10. Applied rewrites 55.8%

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

   if -2.54999999999999999e69 < a < 2.5000000000000001e-4

   1. Initial program 68.2%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. mul-1-neg N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 48.4

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

   5. Applied rewrites 48.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 19.0%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 65.8%

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

Alternative 10: 55.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{x}{z}, t\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+28}:\\ \;\;\;\;\mathsf{fma}\left(-x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ x z) t)))
   (if (<= z -2.6e+81) t_1 (if (<= z 2.2e+28) (fma (- x) (/ y a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, (x / z), t);
	double tmp;
	if (z <= -2.6e+81) {
		tmp = t_1;
	} else if (z <= 2.2e+28) {
		tmp = fma(-x, (y / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(x / z), t)
	tmp = 0.0
	if (z <= -2.6e+81)
		tmp = t_1;
	elseif (z <= 2.2e+28)
		tmp = fma(Float64(-x), Float64(y / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(x / z), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[z, -2.6e+81], t$95$1, If[LessEqual[z, 2.2e+28], N[((-x) * N[(y / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.59999999999999992e81 or 2.19999999999999986e28 < z

   1. Initial program 36.5%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. mul-1-neg N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 41.5

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

   5. Applied rewrites 41.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 10.1%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 69.0%

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

   12. Taylor expanded in x around inf

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

   14. Applied rewrites 62.5%

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

   if -2.59999999999999992e81 < z < 2.19999999999999986e28

   1. Initial program 92.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 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 z around 0

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

      1. lower-/.f64 73.7

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

   7. Applied rewrites 73.7%

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

   8. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 55.8

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

   10. Applied rewrites 55.8%

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

Alternative 11: 51.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, \frac{z}{a}, x\right)\\ \mathbf{if}\;a \leq -2.9 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 0.00026:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{x}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma x (/ z a) x)))
   (if (<= a -2.9e+69) t_1 (if (<= a 0.00026) (fma y (/ x z) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(x, (z / a), x);
	double tmp;
	if (a <= -2.9e+69) {
		tmp = t_1;
	} else if (a <= 0.00026) {
		tmp = fma(y, (x / z), t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(x, Float64(z / a), x)
	tmp = 0.0
	if (a <= -2.9e+69)
		tmp = t_1;
	elseif (a <= 0.00026)
		tmp = fma(y, Float64(x / z), t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(z / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -2.9e+69], t$95$1, If[LessEqual[a, 0.00026], N[(y * N[(x / z), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.8999999999999998e69 or 2.59999999999999977e-4 < a

   1. Initial program 71.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lower-/.f64 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. remove-double-neg N/A

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

      14. lower-+.f64 N/A

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

      15. lower-neg.f64 67.5

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

   5. Applied rewrites 67.5%

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

   7. Applied rewrites 57.8%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 49.6%

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

   11. Taylor expanded in z around 0

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

   13. Applied rewrites 49.0%

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

   if -2.8999999999999998e69 < a < 2.59999999999999977e-4

   1. Initial program 68.2%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. mul-1-neg N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 48.4

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

   5. Applied rewrites 48.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 19.0%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 65.8%

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

   12. Taylor expanded in x around inf

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

   14. Applied rewrites 54.9%

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

Alternative 12: 26.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-62}:\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= x -3.8e+40) t_1 (if (<= x 1.75e-62) (+ x (- t x)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (x <= -3.8e+40) {
		tmp = t_1;
	} else if (x <= 1.75e-62) {
		tmp = x + (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 = x * (y / z)
    if (x <= (-3.8d+40)) then
        tmp = t_1
    else if (x <= 1.75d-62) then
        tmp = x + (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 = x * (y / z);
	double tmp;
	if (x <= -3.8e+40) {
		tmp = t_1;
	} else if (x <= 1.75e-62) {
		tmp = x + (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if x <= -3.8e+40:
		tmp = t_1
	elif x <= 1.75e-62:
		tmp = x + (t - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (x <= -3.8e+40)
		tmp = t_1;
	elseif (x <= 1.75e-62)
		tmp = Float64(x + Float64(t - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (x <= -3.8e+40)
		tmp = t_1;
	elseif (x <= 1.75e-62)
		tmp = x + (t - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.8e+40], t$95$1, If[LessEqual[x, 1.75e-62], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.80000000000000004e40 or 1.7500000000000001e-62 < x

   1. Initial program 61.6%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. mul-1-neg N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 29.9

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

   5. Applied rewrites 29.9%

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

   6. Taylor expanded in x around -inf

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

   8. Applied rewrites 23.3%

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

   10. Applied rewrites 24.9%

       \[\leadsto \frac{y}{z} \cdot x \]

   if -3.80000000000000004e40 < x < 1.7500000000000001e-62

   1. Initial program 80.8%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 26.2

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

   5. Applied rewrites 26.2%

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

4. Final simplification 25.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-62}:\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 26.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-62}:\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ x z))))
   (if (<= x -3.8e+40) t_1 (if (<= x 1.75e-62) (+ x (- t x)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (x / z);
	double tmp;
	if (x <= -3.8e+40) {
		tmp = t_1;
	} else if (x <= 1.75e-62) {
		tmp = x + (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 = y * (x / z)
    if (x <= (-3.8d+40)) then
        tmp = t_1
    else if (x <= 1.75d-62) then
        tmp = x + (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 = y * (x / z);
	double tmp;
	if (x <= -3.8e+40) {
		tmp = t_1;
	} else if (x <= 1.75e-62) {
		tmp = x + (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (x / z)
	tmp = 0
	if x <= -3.8e+40:
		tmp = t_1
	elif x <= 1.75e-62:
		tmp = x + (t - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (x <= -3.8e+40)
		tmp = t_1;
	elseif (x <= 1.75e-62)
		tmp = Float64(x + Float64(t - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (x / z);
	tmp = 0.0;
	if (x <= -3.8e+40)
		tmp = t_1;
	elseif (x <= 1.75e-62)
		tmp = x + (t - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.8e+40], t$95$1, If[LessEqual[x, 1.75e-62], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.80000000000000004e40 or 1.7500000000000001e-62 < x

   1. Initial program 61.6%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. mul-1-neg N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 29.9

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

   5. Applied rewrites 29.9%

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

   6. Taylor expanded in x around -inf

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

   8. Applied rewrites 23.3%

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

   10. Applied rewrites 24.3%

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

   if -3.80000000000000004e40 < x < 1.7500000000000001e-62

   1. Initial program 80.8%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 26.2

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

   5. Applied rewrites 26.2%

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

Alternative 14: 40.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, \frac{x}{z}, t\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 69.9%

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

3. Taylor expanded in a around 0

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

   1. +-commutative N/A

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

   2. mul-1-neg N/A

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

   3. associate-/l* N/A

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

   4. distribute-rgt-neg-in N/A

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

   5. lower-fma.f64 N/A

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

   6. lower--.f64 N/A

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

   7. distribute-neg-frac N/A

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

   8. mul-1-neg N/A

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

   9. lower-/.f64 N/A

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

   10. mul-1-neg N/A

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

   11. sub-neg N/A

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

   12. +-commutative N/A

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

   13. distribute-neg-in N/A

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

   14. unsub-neg N/A

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

   15. remove-double-neg N/A

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

   16. lower--.f64 33.7

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

5. Applied rewrites 33.7%

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

6. Taylor expanded in t around 0

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

8. Applied rewrites 13.3%

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

9. Taylor expanded in z around inf

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

11. Applied rewrites 44.4%

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

12. Taylor expanded in x around inf

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

14. Applied rewrites 36.3%

    \[\leadsto \mathsf{fma}\left(y, \frac{x}{z}, t\right) \]
15. Add Preprocessing

Alternative 15: 19.3% 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 69.9%

   \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
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 15.2

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

5. Applied rewrites 15.2%

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

Alternative 16: 2.8% accurate, 29.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

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 = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 69.9%

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

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. mul-1-neg N/A

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

   3. *-commutative N/A

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

   4. associate-/l* N/A

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

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

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

   6. lower-fma.f64 N/A

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

   7. lower--.f64 N/A

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

   8. distribute-neg-frac2 N/A

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

   9. lower-/.f64 N/A

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

   10. sub-neg N/A

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

   11. +-commutative N/A

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

   12. distribute-neg-in N/A

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

   13. remove-double-neg N/A

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

   14. lower-+.f64 N/A

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

   15. lower-neg.f64 47.4

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

5. Applied rewrites 47.4%

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

7. Applied rewrites 40.3%

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

8. Taylor expanded in t around 0

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

10. Applied rewrites 28.8%

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

11. Taylor expanded in z around inf

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

13. Applied rewrites 2.8%

    \[\leadsto 0 \]
14. Add Preprocessing

Developer Target 1: 83.4% 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 2024233 
(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))))