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

Percentage Accurate: 68.1% → 87.5%

Time: 10.5s

Alternatives: 15

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+69}:\\ \;\;\;\;y - \left(a - z\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+195}:\\ \;\;\;\;x - \frac{x - y}{\frac{t - a}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{a - z}{t} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.6e+69)
   (- y (* (- a z) (/ (- x y) t)))
   (if (<= t 1.5e+195)
     (- x (/ (- x y) (/ (- t a) (- t z))))
     (- y (* (/ (- a z) t) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.6e+69) {
		tmp = y - ((a - z) * ((x - y) / t));
	} else if (t <= 1.5e+195) {
		tmp = x - ((x - y) / ((t - a) / (t - z)));
	} else {
		tmp = y - (((a - z) / t) * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.6d+69)) then
        tmp = y - ((a - z) * ((x - y) / t))
    else if (t <= 1.5d+195) then
        tmp = x - ((x - y) / ((t - a) / (t - z)))
    else
        tmp = y - (((a - z) / t) * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.6e+69) {
		tmp = y - ((a - z) * ((x - y) / t));
	} else if (t <= 1.5e+195) {
		tmp = x - ((x - y) / ((t - a) / (t - z)));
	} else {
		tmp = y - (((a - z) / t) * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.6e+69:
		tmp = y - ((a - z) * ((x - y) / t))
	elif t <= 1.5e+195:
		tmp = x - ((x - y) / ((t - a) / (t - z)))
	else:
		tmp = y - (((a - z) / t) * x)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.6e+69)
		tmp = Float64(y - Float64(Float64(a - z) * Float64(Float64(x - y) / t)));
	elseif (t <= 1.5e+195)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(Float64(t - a) / Float64(t - z))));
	else
		tmp = Float64(y - Float64(Float64(Float64(a - z) / t) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.6e+69)
		tmp = y - ((a - z) * ((x - y) / t));
	elseif (t <= 1.5e+195)
		tmp = x - ((x - y) / ((t - a) / (t - z)));
	else
		tmp = y - (((a - z) / t) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.6e+69], N[(y - N[(N[(a - z), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e+195], N[(x - N[(N[(x - y), $MachinePrecision] / N[(N[(t - a), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.6000000000000003e69

   1. Initial program 40.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 70.6

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

   4. Applied rewrites 70.6%

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

   5. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. lower--.f64 N/A

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

      7. div-sub N/A

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

      8. associate-/l* N/A

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

      9. associate-/l* N/A

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

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

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. *-lft-identity N/A

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

      15. metadata-eval N/A

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

      16. cancel-sign-sub-inv N/A

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

      17. lower-*.f64 N/A

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

   7. Applied rewrites 88.6%

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

   if -3.6000000000000003e69 < t < 1.5e195

   1. Initial program 81.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 90.1

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

   4. Applied rewrites 90.1%

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

   if 1.5e195 < t

   1. Initial program 27.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 56.2

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

   4. Applied rewrites 56.2%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 6.6

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

   7. Applied rewrites 6.6%

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

   8. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. mul-1-neg N/A

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

      5. div-sub N/A

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

      6. mul-1-neg N/A

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

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

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

   10. Applied rewrites 64.6%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 87.4%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+69}:\\ \;\;\;\;y - \left(a - z\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+195}:\\ \;\;\;\;x - \frac{x - y}{\frac{t - a}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{a - z}{t} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 51.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{t} \cdot z\\ t_2 := \mathsf{fma}\left(a, \frac{y}{t}, y\right)\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+173}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-43}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{elif}\;t \leq 1450:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ (- x y) t) z)) (t_2 (fma a (/ y t) y)))
   (if (<= t -1.6e+173)
     t_2
     (if (<= t -8e-62)
       t_1
       (if (<= t 2.6e-43) (fma (/ y a) z x) (if (<= t 1450.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) / t) * z;
	double t_2 = fma(a, (y / t), y);
	double tmp;
	if (t <= -1.6e+173) {
		tmp = t_2;
	} else if (t <= -8e-62) {
		tmp = t_1;
	} else if (t <= 2.6e-43) {
		tmp = fma((y / a), z, x);
	} else if (t <= 1450.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) / t) * z)
	t_2 = fma(a, Float64(y / t), y)
	tmp = 0.0
	if (t <= -1.6e+173)
		tmp = t_2;
	elseif (t <= -8e-62)
		tmp = t_1;
	elseif (t <= 2.6e-43)
		tmp = fma(Float64(y / a), z, x);
	elseif (t <= 1450.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y / t), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t, -1.6e+173], t$95$2, If[LessEqual[t, -8e-62], t$95$1, If[LessEqual[t, 2.6e-43], N[(N[(y / a), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[t, 1450.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6000000000000001e173 or 1450 < t

   1. Initial program 40.2%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. unsub-neg N/A

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

      13. remove-double-neg N/A

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

      14. lower--.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 51.2

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

   5. Applied rewrites 51.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 45.4%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 52.8%

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

   if -1.6000000000000001e173 < t < -8.0000000000000003e-62 or 2.6e-43 < t < 1450

   1. Initial program 78.5%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 58.6

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

   5. Applied rewrites 58.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 53.1%

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

   if -8.0000000000000003e-62 < t < 2.6e-43

   1. Initial program 91.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 97.1

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

   4. Applied rewrites 97.1%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 80.0

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

   7. Applied rewrites 80.0%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 64.9%

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

Alternative 3: 33.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot x}{t}\\ t_2 := \mathsf{fma}\left(a, \frac{y}{t}, y\right)\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+172}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-183}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-49}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq 400:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* z x) t)) (t_2 (fma a (/ y t) y)))
   (if (<= t -2.7e+172)
     t_2
     (if (<= t -1.85e-183)
       t_1
       (if (<= t 2.25e-49) (/ (* z y) a) (if (<= t 400.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * x) / t;
	double t_2 = fma(a, (y / t), y);
	double tmp;
	if (t <= -2.7e+172) {
		tmp = t_2;
	} else if (t <= -1.85e-183) {
		tmp = t_1;
	} else if (t <= 2.25e-49) {
		tmp = (z * y) / a;
	} else if (t <= 400.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * x) / t)
	t_2 = fma(a, Float64(y / t), y)
	tmp = 0.0
	if (t <= -2.7e+172)
		tmp = t_2;
	elseif (t <= -1.85e-183)
		tmp = t_1;
	elseif (t <= 2.25e-49)
		tmp = Float64(Float64(z * y) / a);
	elseif (t <= 400.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * x), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y / t), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t, -2.7e+172], t$95$2, If[LessEqual[t, -1.85e-183], t$95$1, If[LessEqual[t, 2.25e-49], N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 400.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7e172 or 400 < t

   1. Initial program 40.2%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. unsub-neg N/A

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

      13. remove-double-neg N/A

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

      14. lower--.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 51.2

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

   5. Applied rewrites 51.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 45.4%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 52.8%

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

   if -2.7e172 < t < -1.8499999999999999e-183 or 2.2500000000000001e-49 < t < 400

   1. Initial program 81.7%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 54.0

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

   5. Applied rewrites 54.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 50.8%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 36.8%

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

   if -1.8499999999999999e-183 < t < 2.2500000000000001e-49

   1. Initial program 91.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 96.4

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

   4. Applied rewrites 96.4%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 83.9

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

   7. Applied rewrites 83.9%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 41.4%

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

Alternative 4: 33.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot x}{t}\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+172}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-183}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-49}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq 400:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* z x) t)))
   (if (<= t -2.7e+172)
     y
     (if (<= t -1.85e-183)
       t_1
       (if (<= t 2.25e-49) (/ (* z y) a) (if (<= t 400.0) t_1 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * x) / t;
	double tmp;
	if (t <= -2.7e+172) {
		tmp = y;
	} else if (t <= -1.85e-183) {
		tmp = t_1;
	} else if (t <= 2.25e-49) {
		tmp = (z * y) / a;
	} else if (t <= 400.0) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * x) / t
    if (t <= (-2.7d+172)) then
        tmp = y
    else if (t <= (-1.85d-183)) then
        tmp = t_1
    else if (t <= 2.25d-49) then
        tmp = (z * y) / a
    else if (t <= 400.0d0) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * x) / t;
	double tmp;
	if (t <= -2.7e+172) {
		tmp = y;
	} else if (t <= -1.85e-183) {
		tmp = t_1;
	} else if (t <= 2.25e-49) {
		tmp = (z * y) / a;
	} else if (t <= 400.0) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z * x) / t
	tmp = 0
	if t <= -2.7e+172:
		tmp = y
	elif t <= -1.85e-183:
		tmp = t_1
	elif t <= 2.25e-49:
		tmp = (z * y) / a
	elif t <= 400.0:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * x) / t)
	tmp = 0.0
	if (t <= -2.7e+172)
		tmp = y;
	elseif (t <= -1.85e-183)
		tmp = t_1;
	elseif (t <= 2.25e-49)
		tmp = Float64(Float64(z * y) / a);
	elseif (t <= 400.0)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * x) / t;
	tmp = 0.0;
	if (t <= -2.7e+172)
		tmp = y;
	elseif (t <= -1.85e-183)
		tmp = t_1;
	elseif (t <= 2.25e-49)
		tmp = (z * y) / a;
	elseif (t <= 400.0)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * x), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -2.7e+172], y, If[LessEqual[t, -1.85e-183], t$95$1, If[LessEqual[t, 2.25e-49], N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 400.0], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7e172 or 400 < t

   1. Initial program 40.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-neg N/A

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

      5. distribute-lft-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-neg.f64 40.1

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

   4. Applied rewrites 40.1%

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

   5. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. *-lft-identity N/A

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

      3. metadata-eval N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. associate--l+ N/A

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

      6. distribute-rgt1-in N/A

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

      7. metadata-eval N/A

         \[\leadsto \color{blue}{0} \cdot x - -1 \cdot y \]

      8. mul0-lft N/A

         \[\leadsto \color{blue}{0} - -1 \cdot y \]

      9. neg-sub0 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(-1 \cdot y\right)} \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

      11. remove-double-neg 51.5

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

   7. Applied rewrites 51.5%

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

   if -2.7e172 < t < -1.8499999999999999e-183 or 2.2500000000000001e-49 < t < 400

   1. Initial program 81.7%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 54.0

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

   5. Applied rewrites 54.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 50.8%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 36.8%

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

   if -1.8499999999999999e-183 < t < 2.2500000000000001e-49

   1. Initial program 91.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 96.4

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

   4. Applied rewrites 96.4%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 83.9

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

   7. Applied rewrites 83.9%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 41.4%

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

Alternative 5: 83.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{t}\\ \mathbf{if}\;t \leq -1.56 \cdot 10^{+69}:\\ \;\;\;\;y - \left(a - z\right) \cdot t\_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+102}:\\ \;\;\;\;x - \frac{\left(t - z\right) \cdot \left(x - y\right)}{t - a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, z - a, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x y) t)))
   (if (<= t -1.56e+69)
     (- y (* (- a z) t_1))
     (if (<= t 7e+102)
       (- x (/ (* (- t z) (- x y)) (- t a)))
       (fma t_1 (- z a) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) / t;
	double tmp;
	if (t <= -1.56e+69) {
		tmp = y - ((a - z) * t_1);
	} else if (t <= 7e+102) {
		tmp = x - (((t - z) * (x - y)) / (t - a));
	} else {
		tmp = fma(t_1, (z - a), y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) / t)
	tmp = 0.0
	if (t <= -1.56e+69)
		tmp = Float64(y - Float64(Float64(a - z) * t_1));
	elseif (t <= 7e+102)
		tmp = Float64(x - Float64(Float64(Float64(t - z) * Float64(x - y)) / Float64(t - a)));
	else
		tmp = fma(t_1, Float64(z - a), y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -1.56e+69], N[(y - N[(N[(a - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+102], N[(x - N[(N[(N[(t - z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[(z - a), $MachinePrecision] + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.56000000000000007e69

   1. Initial program 40.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 70.6

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

   4. Applied rewrites 70.6%

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

   5. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. lower--.f64 N/A

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

      7. div-sub N/A

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

      8. associate-/l* N/A

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

      9. associate-/l* N/A

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

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

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. *-lft-identity N/A

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

      15. metadata-eval N/A

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

      16. cancel-sign-sub-inv N/A

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

      17. lower-*.f64 N/A

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

   7. Applied rewrites 88.6%

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

   if -1.56000000000000007e69 < t < 7.00000000000000021e102

   1. Initial program 88.3%

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

   if 7.00000000000000021e102 < t

   1. Initial program 39.7%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 79.6%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.56 \cdot 10^{+69}:\\ \;\;\;\;y - \left(a - z\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+102}:\\ \;\;\;\;x - \frac{\left(t - z\right) \cdot \left(x - y\right)}{t - a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, z - a, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{z}{t} \cdot y\\ \mathbf{if}\;t \leq -1.12 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-43}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{elif}\;t \leq 400:\\ \;\;\;\;\frac{x - y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* (/ z t) y))))
   (if (<= t -1.12e-60)
     t_1
     (if (<= t 2.6e-43)
       (fma (/ y a) z x)
       (if (<= t 400.0) (* (/ (- x y) t) z) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - ((z / t) * y);
	double tmp;
	if (t <= -1.12e-60) {
		tmp = t_1;
	} else if (t <= 2.6e-43) {
		tmp = fma((y / a), z, x);
	} else if (t <= 400.0) {
		tmp = ((x - y) / t) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(Float64(z / t) * y))
	tmp = 0.0
	if (t <= -1.12e-60)
		tmp = t_1;
	elseif (t <= 2.6e-43)
		tmp = fma(Float64(y / a), z, x);
	elseif (t <= 400.0)
		tmp = Float64(Float64(Float64(x - y) / t) * z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.12e-60], t$95$1, If[LessEqual[t, 2.6e-43], N[(N[(y / a), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[t, 400.0], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.12e-60 or 400 < t

   1. Initial program 51.0%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 54.7

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

   5. Applied rewrites 54.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 37.3%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 55.0%

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

   13. Applied rewrites 55.0%

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

   if -1.12e-60 < t < 2.6e-43

   1. Initial program 90.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 96.1

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

   4. Applied rewrites 96.1%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 79.3

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

   7. Applied rewrites 79.3%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 64.6%

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

   if 2.6e-43 < t < 400

   1. Initial program 84.7%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 62.3

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

   5. Applied rewrites 62.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 70.8%

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

Alternative 7: 77.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x - y}{t}, z - a, y\right)\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-26}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- x y) t) (- z a) y)))
   (if (<= t -2.3e+43)
     t_1
     (if (<= t 6.8e-26) (- x (/ (* (- y x) z) (- t a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((x - y) / t), (z - a), y);
	double tmp;
	if (t <= -2.3e+43) {
		tmp = t_1;
	} else if (t <= 6.8e-26) {
		tmp = x - (((y - x) * z) / (t - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(x - y) / t), Float64(z - a), y)
	tmp = 0.0
	if (t <= -2.3e+43)
		tmp = t_1;
	elseif (t <= 6.8e-26)
		tmp = Float64(x - Float64(Float64(Float64(y - x) * z) / Float64(t - a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t, -2.3e+43], t$95$1, If[LessEqual[t, 6.8e-26], N[(x - N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.3000000000000002e43 or 6.80000000000000026e-26 < t

   1. Initial program 45.9%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 81.8%

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

   if -2.3000000000000002e43 < t < 6.80000000000000026e-26

   1. Initial program 90.2%

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

   3. Taylor expanded in t around 0

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 80.4

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

   5. Applied rewrites 80.4%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, z - a, y\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-26}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, z - a, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, \frac{y}{t}, y\right)\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-38}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{elif}\;t \leq 400:\\ \;\;\;\;\frac{z \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma a (/ y t) y)))
   (if (<= t -1.35e+31)
     t_1
     (if (<= t 1.6e-38)
       (fma (/ y a) z x)
       (if (<= t 400.0) (/ (* z x) t) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(a, (y / t), y);
	double tmp;
	if (t <= -1.35e+31) {
		tmp = t_1;
	} else if (t <= 1.6e-38) {
		tmp = fma((y / a), z, x);
	} else if (t <= 400.0) {
		tmp = (z * x) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(a, Float64(y / t), y)
	tmp = 0.0
	if (t <= -1.35e+31)
		tmp = t_1;
	elseif (t <= 1.6e-38)
		tmp = fma(Float64(y / a), z, x);
	elseif (t <= 400.0)
		tmp = Float64(Float64(z * x) / t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a * N[(y / t), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t, -1.35e+31], t$95$1, If[LessEqual[t, 1.6e-38], N[(N[(y / a), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[t, 400.0], N[(N[(z * x), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.34999999999999993e31 or 400 < t

   1. Initial program 45.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. unsub-neg N/A

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

      13. remove-double-neg N/A

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

      14. lower--.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 48.7

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

   5. Applied rewrites 48.7%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 41.8%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 47.9%

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

   if -1.34999999999999993e31 < t < 1.59999999999999989e-38

   1. Initial program 90.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 95.0

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

   4. Applied rewrites 95.0%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 70.6

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

   7. Applied rewrites 70.6%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 57.8%

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

   if 1.59999999999999989e-38 < t < 400

   1. Initial program 82.1%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 64.1

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

   5. Applied rewrites 64.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 65.6%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 65.0%

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

Alternative 9: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x - y}{t}, z - a, y\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-46}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- x y) t) (- z a) y)))
   (if (<= t -7.5e-61)
     t_1
     (if (<= t 5.6e-46) (fma (/ (- z t) a) (- y x) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((x - y) / t), (z - a), y);
	double tmp;
	if (t <= -7.5e-61) {
		tmp = t_1;
	} else if (t <= 5.6e-46) {
		tmp = fma(((z - t) / a), (y - x), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(x - y) / t), Float64(z - a), y)
	tmp = 0.0
	if (t <= -7.5e-61)
		tmp = t_1;
	elseif (t <= 5.6e-46)
		tmp = fma(Float64(Float64(z - t) / a), Float64(y - x), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t, -7.5e-61], t$95$1, If[LessEqual[t, 5.6e-46], N[(N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.50000000000000047e-61 or 5.5999999999999997e-46 < t

   1. Initial program 53.7%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 78.3%

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

   if -7.50000000000000047e-61 < t < 5.5999999999999997e-46

   1. Initial program 90.2%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 84.4

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

   5. Applied rewrites 84.4%

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

Alternative 10: 73.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x - y}{t}, z - a, y\right)\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-46}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- x y) t) (- z a) y)))
   (if (<= t -5.8e-61) t_1 (if (<= t 5.6e-46) (fma (- y x) (/ z a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((x - y) / t), (z - a), y);
	double tmp;
	if (t <= -5.8e-61) {
		tmp = t_1;
	} else if (t <= 5.6e-46) {
		tmp = fma((y - x), (z / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(x - y) / t), Float64(z - a), y)
	tmp = 0.0
	if (t <= -5.8e-61)
		tmp = t_1;
	elseif (t <= 5.6e-46)
		tmp = fma(Float64(y - x), Float64(z / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t, -5.8e-61], t$95$1, If[LessEqual[t, 5.6e-46], N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.7999999999999999e-61 or 5.5999999999999997e-46 < t

   1. Initial program 53.7%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 78.3%

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

   if -5.7999999999999999e-61 < t < 5.5999999999999997e-46

   1. Initial program 90.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 96.1

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

   4. Applied rewrites 96.1%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 79.3

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

   7. Applied rewrites 79.3%

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

   9. Applied rewrites 80.3%

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

Alternative 11: 69.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x - y}{t}, z, y\right)\\ \mathbf{if}\;t \leq -8 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-43}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- x y) t) z y)))
   (if (<= t -8e-62) t_1 (if (<= t 2.75e-43) (fma (- y x) (/ z a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((x - y) / t), z, y);
	double tmp;
	if (t <= -8e-62) {
		tmp = t_1;
	} else if (t <= 2.75e-43) {
		tmp = fma((y - x), (z / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(x - y) / t), z, y)
	tmp = 0.0
	if (t <= -8e-62)
		tmp = t_1;
	elseif (t <= 2.75e-43)
		tmp = fma(Float64(y - x), Float64(z / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * z + y), $MachinePrecision]}, If[LessEqual[t, -8e-62], t$95$1, If[LessEqual[t, 2.75e-43], N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.0000000000000003e-62 or 2.75000000000000006e-43 < t

   1. Initial program 53.7%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 54.7

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

   5. Applied rewrites 54.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 38.9%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 52.0%

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

   12. Taylor expanded in t around inf

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

   14. Applied rewrites 70.9%

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

   if -8.0000000000000003e-62 < t < 2.75000000000000006e-43

   1. Initial program 91.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 97.1

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

   4. Applied rewrites 97.1%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 80.0

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

   7. Applied rewrites 80.0%

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

   9. Applied rewrites 81.0%

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

Alternative 12: 68.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x - y}{t}, z, y\right)\\ \mathbf{if}\;t \leq -7.4 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-43}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{a}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- x y) t) z y)))
   (if (<= t -7.4e-62) t_1 (if (<= t 2.75e-43) (fma (/ (- y x) a) z x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((x - y) / t), z, y);
	double tmp;
	if (t <= -7.4e-62) {
		tmp = t_1;
	} else if (t <= 2.75e-43) {
		tmp = fma(((y - x) / a), z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(x - y) / t), z, y)
	tmp = 0.0
	if (t <= -7.4e-62)
		tmp = t_1;
	elseif (t <= 2.75e-43)
		tmp = fma(Float64(Float64(y - x) / a), z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * z + y), $MachinePrecision]}, If[LessEqual[t, -7.4e-62], t$95$1, If[LessEqual[t, 2.75e-43], N[(N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] * z + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.3999999999999996e-62 or 2.75000000000000006e-43 < t

   1. Initial program 53.7%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 54.7

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

   5. Applied rewrites 54.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 38.9%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 52.0%

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

   12. Taylor expanded in t around inf

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

   14. Applied rewrites 70.9%

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

   if -7.3999999999999996e-62 < t < 2.75000000000000006e-43

   1. Initial program 91.1%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 80.0

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

   5. Applied rewrites 80.0%

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

Alternative 13: 63.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x - y}{t}, z, y\right)\\ \mathbf{if}\;t \leq -7.4 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-46}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- x y) t) z y)))
   (if (<= t -7.4e-62) t_1 (if (<= t 3.8e-46) (fma (/ y a) z x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((x - y) / t), z, y);
	double tmp;
	if (t <= -7.4e-62) {
		tmp = t_1;
	} else if (t <= 3.8e-46) {
		tmp = fma((y / a), z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(x - y) / t), z, y)
	tmp = 0.0
	if (t <= -7.4e-62)
		tmp = t_1;
	elseif (t <= 3.8e-46)
		tmp = fma(Float64(y / a), z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * z + y), $MachinePrecision]}, If[LessEqual[t, -7.4e-62], t$95$1, If[LessEqual[t, 3.8e-46], N[(N[(y / a), $MachinePrecision] * z + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.3999999999999996e-62 or 3.7999999999999997e-46 < t

   1. Initial program 53.7%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 54.7

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

   5. Applied rewrites 54.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 38.9%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 52.0%

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

   12. Taylor expanded in t around inf

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

   14. Applied rewrites 70.9%

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

   if -7.3999999999999996e-62 < t < 3.7999999999999997e-46

   1. Initial program 91.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 97.1

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

   4. Applied rewrites 97.1%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 80.0

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

   7. Applied rewrites 80.0%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 64.9%

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

Alternative 14: 31.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t} \cdot x\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 120000:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ z t) x)))
   (if (<= z -7.2e+62) t_1 (if (<= z 120000.0) y t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z / t) * x;
	double tmp;
	if (z <= -7.2e+62) {
		tmp = t_1;
	} else if (z <= 120000.0) {
		tmp = y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / t) * x
    if (z <= (-7.2d+62)) then
        tmp = t_1
    else if (z <= 120000.0d0) then
        tmp = y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z / t) * x;
	double tmp;
	if (z <= -7.2e+62) {
		tmp = t_1;
	} else if (z <= 120000.0) {
		tmp = y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z / t) * x
	tmp = 0
	if z <= -7.2e+62:
		tmp = t_1
	elif z <= 120000.0:
		tmp = y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z / t) * x)
	tmp = 0.0
	if (z <= -7.2e+62)
		tmp = t_1;
	elseif (z <= 120000.0)
		tmp = y;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z / t) * x;
	tmp = 0.0;
	if (z <= -7.2e+62)
		tmp = t_1;
	elseif (z <= 120000.0)
		tmp = y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -7.2e+62], t$95$1, If[LessEqual[z, 120000.0], y, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.2e62 or 1.2e5 < z

   1. Initial program 73.0%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 53.9

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

   5. Applied rewrites 53.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 37.0%

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

   if -7.2e62 < z < 1.2e5

   1. Initial program 62.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-neg N/A

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

      5. distribute-lft-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-neg.f64 62.0

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

   4. Applied rewrites 62.0%

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

   5. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. *-lft-identity N/A

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

      3. metadata-eval N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. associate--l+ N/A

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

      6. distribute-rgt1-in N/A

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

      7. metadata-eval N/A

         \[\leadsto \color{blue}{0} \cdot x - -1 \cdot y \]

      8. mul0-lft N/A

         \[\leadsto \color{blue}{0} - -1 \cdot y \]

      9. neg-sub0 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(-1 \cdot y\right)} \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

      11. remove-double-neg 38.2

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

   7. Applied rewrites 38.2%

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

Alternative 15: 25.1% accurate, 29.0× speedup

Math

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

FPCore

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

C

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

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 = y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 67.0%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift--.f64 N/A

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

   4. sub-neg N/A

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

   5. distribute-lft-in N/A

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

   6. lower-fma.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. lower-neg.f64 66.5

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

4. Applied rewrites 66.5%

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

5. Taylor expanded in t around inf

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

   1. +-commutative N/A

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

   2. *-lft-identity N/A

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

   3. metadata-eval N/A

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

   4. cancel-sign-sub-inv N/A

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

   5. associate--l+ N/A

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

   6. distribute-rgt1-in N/A

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

   7. metadata-eval N/A

      \[\leadsto \color{blue}{0} \cdot x - -1 \cdot y \]

   8. mul0-lft N/A

      \[\leadsto \color{blue}{0} - -1 \cdot y \]

   9. neg-sub0 N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(-1 \cdot y\right)} \]

   10. mul-1-neg N/A

       \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

   11. remove-double-neg 26.8

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

7. Applied rewrites 26.8%

   \[\leadsto \color{blue}{y} \]
8. Add Preprocessing

Developer Target 1: 86.5% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024254 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

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

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