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

Percentage Accurate: 67.6% → 90.9%

Time: 13.5s

Alternatives: 25

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: 67.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{\frac{a - t}{z - t}}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-300}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{z - a}{t}, y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y x) (/ (- a t) (- z t)))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 -5e-300)
     t_1
     (if (<= t_2 0.0) (fma (- x y) (/ (- z a) t) y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / ((a - t) / (z - t)));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -5e-300) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = fma((x - y), ((z - a) / t), y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -5e-300)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = fma(Float64(x - y), Float64(Float64(z - a) / t), y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-300], t$95$1, If[LessEqual[t$95$2, 0.0], N[(N[(x - y), $MachinePrecision] * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] + y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.99999999999999996e-300 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 72.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 89.1

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

   4. Applied rewrites 89.1%

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

   if -4.99999999999999996e-300 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.2%

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 99.8%

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

Alternative 2: 90.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-300}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{z - a}{t}, y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- z t) (- a t)) (- y x) x))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 -5e-300)
     t_1
     (if (<= t_2 0.0) (fma (- x y) (/ (- z a) t) y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((z - t) / (a - t)), (y - x), x);
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -5e-300) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = fma((x - y), ((z - a) / t), y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(z - t) / Float64(a - t)), Float64(y - x), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -5e-300)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = fma(Float64(x - y), Float64(Float64(z - a) / t), y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-300], t$95$1, If[LessEqual[t$95$2, 0.0], N[(N[(x - y), $MachinePrecision] * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] + y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.99999999999999996e-300 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 72.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 88.9

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

   4. Applied rewrites 88.9%

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

   if -4.99999999999999996e-300 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.2%

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 99.8%

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

Alternative 3: 37.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{z}\\ \mathbf{if}\;t \leq -4 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -0.00041:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-307}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-257}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{x}{a}, x\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+108}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y z))))
   (if (<= t -4e+151)
     t_1
     (if (<= t -0.00041)
       (/ (* z (- x y)) t)
       (if (<= t -8e-307)
         (* (- y x) (/ z a))
         (if (<= t 6.4e-257)
           (fma t (/ x a) x)
           (if (<= t 1.8e+108) (* z (/ (- y x) a)) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / z);
	double tmp;
	if (t <= -4e+151) {
		tmp = t_1;
	} else if (t <= -0.00041) {
		tmp = (z * (x - y)) / t;
	} else if (t <= -8e-307) {
		tmp = (y - x) * (z / a);
	} else if (t <= 6.4e-257) {
		tmp = fma(t, (x / a), x);
	} else if (t <= 1.8e+108) {
		tmp = z * ((y - x) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / z))
	tmp = 0.0
	if (t <= -4e+151)
		tmp = t_1;
	elseif (t <= -0.00041)
		tmp = Float64(Float64(z * Float64(x - y)) / t);
	elseif (t <= -8e-307)
		tmp = Float64(Float64(y - x) * Float64(z / a));
	elseif (t <= 6.4e-257)
		tmp = fma(t, Float64(x / a), x);
	elseif (t <= 1.8e+108)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4e+151], t$95$1, If[LessEqual[t, -0.00041], N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, -8e-307], N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.4e-257], N[(t * N[(x / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 1.8e+108], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.00000000000000007e151 or 1.8e108 < t

   1. Initial program 41.9%

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

   3. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. associate-+r+ N/A

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

      3. associate-+l+ N/A

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

   5. Applied rewrites 65.0%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 41.9%

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

   if -4.00000000000000007e151 < t < -4.0999999999999999e-4

   1. Initial program 56.4%

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 75.6%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 41.8%

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

   if -4.0999999999999999e-4 < t < -7.99999999999999927e-307

   1. Initial program 89.2%

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

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 83.8

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

   5. Applied rewrites 83.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 56.7%

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

   10. Applied rewrites 59.2%

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

   if -7.99999999999999927e-307 < t < 6.39999999999999971e-257

   1. Initial program 100.0%

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

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 92.3

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

   5. Applied rewrites 92.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 71.7%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 70.7%

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

   if 6.39999999999999971e-257 < t < 1.8e108

   1. Initial program 83.3%

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

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 64.6

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

   5. Applied rewrites 64.6%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 13.2%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 46.6%

       \[\leadsto z \cdot \color{blue}{\frac{y - x}{a}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 4: 33.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(z - a\right)}{t}\\ t_2 := z \cdot \frac{y}{z}\\ \mathbf{if}\;t \leq -3 \cdot 10^{+150}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -0.31:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-131}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-72}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{x}{a}, x\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x (- z a)) t)) (t_2 (* z (/ y z))))
   (if (<= t -3e+150)
     t_2
     (if (<= t -0.31)
       t_1
       (if (<= t -2.7e-131)
         (/ (* y z) a)
         (if (<= t 4.4e-72)
           (fma t (/ x a) x)
           (if (<= t 1.9e+129) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * (z - a)) / t;
	double t_2 = z * (y / z);
	double tmp;
	if (t <= -3e+150) {
		tmp = t_2;
	} else if (t <= -0.31) {
		tmp = t_1;
	} else if (t <= -2.7e-131) {
		tmp = (y * z) / a;
	} else if (t <= 4.4e-72) {
		tmp = fma(t, (x / a), x);
	} else if (t <= 1.9e+129) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * Float64(z - a)) / t)
	t_2 = Float64(z * Float64(y / z))
	tmp = 0.0
	if (t <= -3e+150)
		tmp = t_2;
	elseif (t <= -0.31)
		tmp = t_1;
	elseif (t <= -2.7e-131)
		tmp = Float64(Float64(y * z) / a);
	elseif (t <= 4.4e-72)
		tmp = fma(t, Float64(x / a), x);
	elseif (t <= 1.9e+129)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3e+150], t$95$2, If[LessEqual[t, -0.31], t$95$1, If[LessEqual[t, -2.7e-131], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 4.4e-72], N[(t * N[(x / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 1.9e+129], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.00000000000000012e150 or 1.90000000000000003e129 < 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 inf

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

      1. sub-neg N/A

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

      2. associate-+r+ N/A

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

      3. associate-+l+ N/A

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

   5. Applied rewrites 64.4%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 42.7%

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

   if -3.00000000000000012e150 < t < -0.309999999999999998 or 4.40000000000000005e-72 < t < 1.90000000000000003e129

   1. Initial program 67.6%

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 75.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 34.7%

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

   if -0.309999999999999998 < t < -2.70000000000000021e-131

   1. Initial program 88.8%

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

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 67.6

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

   5. Applied rewrites 67.6%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 56.2%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 50.4%

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

   if -2.70000000000000021e-131 < t < 4.40000000000000005e-72

   1. Initial program 91.5%

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

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 85.3

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

   5. Applied rewrites 85.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 61.5%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 43.4%

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

Alternative 5: 47.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(x - y\right)}{t}\\ t_2 := z \cdot \frac{y}{z}\\ \mathbf{if}\;t \leq -4 \cdot 10^{+151}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -15.8:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* z (- x y)) t)) (t_2 (* z (/ y z))))
   (if (<= t -4e+151)
     t_2
     (if (<= t -15.8)
       t_1
       (if (<= t 1.35e-39)
         (+ x (/ (* y z) a))
         (if (<= t 3.9e+129) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * (x - y)) / t;
	double t_2 = z * (y / z);
	double tmp;
	if (t <= -4e+151) {
		tmp = t_2;
	} else if (t <= -15.8) {
		tmp = t_1;
	} else if (t <= 1.35e-39) {
		tmp = x + ((y * z) / a);
	} else if (t <= 3.9e+129) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (z * (x - y)) / t
    t_2 = z * (y / z)
    if (t <= (-4d+151)) then
        tmp = t_2
    else if (t <= (-15.8d0)) then
        tmp = t_1
    else if (t <= 1.35d-39) then
        tmp = x + ((y * z) / a)
    else if (t <= 3.9d+129) then
        tmp = t_1
    else
        tmp = t_2
    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 - y)) / t;
	double t_2 = z * (y / z);
	double tmp;
	if (t <= -4e+151) {
		tmp = t_2;
	} else if (t <= -15.8) {
		tmp = t_1;
	} else if (t <= 1.35e-39) {
		tmp = x + ((y * z) / a);
	} else if (t <= 3.9e+129) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z * (x - y)) / t
	t_2 = z * (y / z)
	tmp = 0
	if t <= -4e+151:
		tmp = t_2
	elif t <= -15.8:
		tmp = t_1
	elif t <= 1.35e-39:
		tmp = x + ((y * z) / a)
	elif t <= 3.9e+129:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * Float64(x - y)) / t)
	t_2 = Float64(z * Float64(y / z))
	tmp = 0.0
	if (t <= -4e+151)
		tmp = t_2;
	elseif (t <= -15.8)
		tmp = t_1;
	elseif (t <= 1.35e-39)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t <= 3.9e+129)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * (x - y)) / t;
	t_2 = z * (y / z);
	tmp = 0.0;
	if (t <= -4e+151)
		tmp = t_2;
	elseif (t <= -15.8)
		tmp = t_1;
	elseif (t <= 1.35e-39)
		tmp = x + ((y * z) / a);
	elseif (t <= 3.9e+129)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4e+151], t$95$2, If[LessEqual[t, -15.8], t$95$1, If[LessEqual[t, 1.35e-39], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e+129], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.00000000000000007e151 or 3.8999999999999997e129 < t

   1. Initial program 39.4%

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

   3. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. associate-+r+ N/A

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

      3. associate-+l+ N/A

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

   5. Applied rewrites 63.9%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 43.1%

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

   if -4.00000000000000007e151 < t < -15.800000000000001 or 1.35e-39 < t < 3.8999999999999997e129

   1. Initial program 65.5%

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 75.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 40.3%

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

   if -15.800000000000001 < t < 1.35e-39

   1. Initial program 90.8%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 75.2

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

   5. Applied rewrites 75.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 64.2%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+151}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq -15.8:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+129}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 43.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z}{a}, -x, x\right)\\ \mathbf{if}\;a \leq -3.1 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-153}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-221}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 3.35 \cdot 10^{-9}:\\ \;\;\;\;x + \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ z a) (- x) x)))
   (if (<= a -3.1e+131)
     t_1
     (if (<= a -3.8e-153)
       (* z (/ (- y x) a))
       (if (<= a 1.5e-221)
         (/ (* z (- x y)) t)
         (if (<= a 3.35e-9) (+ x (- y x)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((z / a), -x, x);
	double tmp;
	if (a <= -3.1e+131) {
		tmp = t_1;
	} else if (a <= -3.8e-153) {
		tmp = z * ((y - x) / a);
	} else if (a <= 1.5e-221) {
		tmp = (z * (x - y)) / t;
	} else if (a <= 3.35e-9) {
		tmp = x + (y - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(z / a), Float64(-x), x)
	tmp = 0.0
	if (a <= -3.1e+131)
		tmp = t_1;
	elseif (a <= -3.8e-153)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (a <= 1.5e-221)
		tmp = Float64(Float64(z * Float64(x - y)) / t);
	elseif (a <= 3.35e-9)
		tmp = Float64(x + Float64(y - x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z / a), $MachinePrecision] * (-x) + x), $MachinePrecision]}, If[LessEqual[a, -3.1e+131], t$95$1, If[LessEqual[a, -3.8e-153], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e-221], N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 3.35e-9], N[(x + N[(y - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.10000000000000016e131 or 3.34999999999999981e-9 < a

   1. Initial program 63.6%

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

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 71.6

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

   5. Applied rewrites 71.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 52.1%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 52.3%

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

   if -3.10000000000000016e131 < a < -3.80000000000000023e-153

   1. Initial program 74.3%

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

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 60.2

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

   5. Applied rewrites 60.2%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 6.2%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 46.1%

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

   if -3.80000000000000023e-153 < a < 1.5000000000000001e-221

   1. Initial program 76.3%

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 89.5%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 57.4%

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

   if 1.5000000000000001e-221 < a < 3.34999999999999981e-9

   1. Initial program 62.0%

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

   3. Taylor expanded in t around inf

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

      1. lower--.f64 40.4

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

   5. Applied rewrites 40.4%

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

Alternative 7: 37.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{z}\\ \mathbf{if}\;t \leq -4 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -0.00041:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+108}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y z))))
   (if (<= t -4e+151)
     t_1
     (if (<= t -0.00041)
       (/ (* z (- x y)) t)
       (if (<= t 1.8e+108) (* z (/ (- y x) a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / z);
	double tmp;
	if (t <= -4e+151) {
		tmp = t_1;
	} else if (t <= -0.00041) {
		tmp = (z * (x - y)) / t;
	} else if (t <= 1.8e+108) {
		tmp = z * ((y - x) / a);
	} 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 * (y / z)
    if (t <= (-4d+151)) then
        tmp = t_1
    else if (t <= (-0.00041d0)) then
        tmp = (z * (x - y)) / t
    else if (t <= 1.8d+108) then
        tmp = z * ((y - x) / a)
    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 * (y / z);
	double tmp;
	if (t <= -4e+151) {
		tmp = t_1;
	} else if (t <= -0.00041) {
		tmp = (z * (x - y)) / t;
	} else if (t <= 1.8e+108) {
		tmp = z * ((y - x) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / z)
	tmp = 0
	if t <= -4e+151:
		tmp = t_1
	elif t <= -0.00041:
		tmp = (z * (x - y)) / t
	elif t <= 1.8e+108:
		tmp = z * ((y - x) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / z))
	tmp = 0.0
	if (t <= -4e+151)
		tmp = t_1;
	elseif (t <= -0.00041)
		tmp = Float64(Float64(z * Float64(x - y)) / t);
	elseif (t <= 1.8e+108)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / z);
	tmp = 0.0;
	if (t <= -4e+151)
		tmp = t_1;
	elseif (t <= -0.00041)
		tmp = (z * (x - y)) / t;
	elseif (t <= 1.8e+108)
		tmp = z * ((y - x) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4e+151], t$95$1, If[LessEqual[t, -0.00041], N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 1.8e+108], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.00000000000000007e151 or 1.8e108 < t

   1. Initial program 41.9%

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

   3. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. associate-+r+ N/A

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

      3. associate-+l+ N/A

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

   5. Applied rewrites 65.0%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 41.9%

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

   if -4.00000000000000007e151 < t < -4.0999999999999999e-4

   1. Initial program 56.4%

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 75.6%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 41.8%

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

   if -4.0999999999999999e-4 < t < 1.8e108

   1. Initial program 87.1%

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

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 74.4

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

   5. Applied rewrites 74.4%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 10.7%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 47.6%

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

Alternative 8: 75.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.0011:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-48}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{z - a}{t}, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -0.0011)
   (+ y (* (- y x) (/ (- a z) t)))
   (if (<= t 1.9e-48)
     (+ x (* (- z t) (/ (- y x) a)))
     (fma (- x y) (/ (- z a) t) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -0.0011) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else if (t <= 1.9e-48) {
		tmp = x + ((z - t) * ((y - x) / a));
	} else {
		tmp = fma((x - y), ((z - a) / t), y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -0.0011)
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	elseif (t <= 1.9e-48)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / a)));
	else
		tmp = fma(Float64(x - y), Float64(Float64(z - a) / t), y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -0.0011], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-48], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -0.00110000000000000007

   1. Initial program 50.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. clear-num N/A

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

      5. associate-/r/ N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 50.2

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

   4. Applied rewrites 50.2%

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

   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. distribute-rgt-out-- N/A

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

      8. associate-/l* N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. *-lft-identity N/A

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

      13. metadata-eval N/A

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

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

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

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

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

      16. associate-*r/ N/A

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

      17. lower-*.f64 N/A

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

   7. Applied rewrites 80.3%

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

   if -0.00110000000000000007 < t < 1.90000000000000001e-48

   1. Initial program 90.5%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 83.0

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

   5. Applied rewrites 83.0%

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

   if 1.90000000000000001e-48 < t

   1. Initial program 53.4%

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 77.4%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.0011:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-48}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{z - a}{t}, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 39.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, \frac{x}{a}, x\right)\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-221}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+43}:\\ \;\;\;\;x + \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma t (/ x a) x)))
   (if (<= a -1.05e+57)
     t_1
     (if (<= a 1.5e-221)
       (/ (* z (- x y)) t)
       (if (<= a 5e+43) (+ x (- y x)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(t, (x / a), x);
	double tmp;
	if (a <= -1.05e+57) {
		tmp = t_1;
	} else if (a <= 1.5e-221) {
		tmp = (z * (x - y)) / t;
	} else if (a <= 5e+43) {
		tmp = x + (y - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(t, Float64(x / a), x)
	tmp = 0.0
	if (a <= -1.05e+57)
		tmp = t_1;
	elseif (a <= 1.5e-221)
		tmp = Float64(Float64(z * Float64(x - y)) / t);
	elseif (a <= 5e+43)
		tmp = Float64(x + Float64(y - x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(x / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -1.05e+57], t$95$1, If[LessEqual[a, 1.5e-221], N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 5e+43], N[(x + N[(y - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.04999999999999995e57 or 5.0000000000000004e43 < a

   1. Initial program 63.2%

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

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 74.0

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

   5. Applied rewrites 74.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 50.4%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 37.7%

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

   if -1.04999999999999995e57 < a < 1.5000000000000001e-221

   1. Initial program 75.7%

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 75.7%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 45.4%

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

   if 1.5000000000000001e-221 < a < 5.0000000000000004e43

   1. Initial program 65.3%

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

   3. Taylor expanded in t around inf

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

      1. lower--.f64 39.5

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

   5. Applied rewrites 39.5%

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

Alternative 10: 75.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.0011:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-48}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{z - a}{t}, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -0.0011)
   (+ y (* (- y x) (/ (- a z) t)))
   (if (<= t 1.9e-48)
     (fma (- z t) (/ (- y x) a) x)
     (fma (- x y) (/ (- z a) t) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -0.0011) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else if (t <= 1.9e-48) {
		tmp = fma((z - t), ((y - x) / a), x);
	} else {
		tmp = fma((x - y), ((z - a) / t), y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -0.0011)
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	elseif (t <= 1.9e-48)
		tmp = fma(Float64(z - t), Float64(Float64(y - x) / a), x);
	else
		tmp = fma(Float64(x - y), Float64(Float64(z - a) / t), y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -0.0011], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-48], N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -0.00110000000000000007

   1. Initial program 50.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. clear-num N/A

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

      5. associate-/r/ N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 50.2

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

   4. Applied rewrites 50.2%

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

   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. distribute-rgt-out-- N/A

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

      8. associate-/l* N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. *-lft-identity N/A

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

      13. metadata-eval N/A

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

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

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

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

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

      16. associate-*r/ N/A

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

      17. lower-*.f64 N/A

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

   7. Applied rewrites 80.3%

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

   if -0.00110000000000000007 < t < 1.90000000000000001e-48

   1. Initial program 90.5%

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

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 82.9

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

   5. Applied rewrites 82.9%

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

   if 1.90000000000000001e-48 < t

   1. Initial program 53.4%

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 77.4%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.0011:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-48}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{z - a}{t}, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x - y, \frac{z - a}{t}, y\right)\\ \mathbf{if}\;t \leq -0.0011:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-48}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- x y) (/ (- z a) t) y)))
   (if (<= t -0.0011)
     t_1
     (if (<= t 1.9e-48) (fma (- z t) (/ (- y x) a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x - y), ((z - a) / t), y);
	double tmp;
	if (t <= -0.0011) {
		tmp = t_1;
	} else if (t <= 1.9e-48) {
		tmp = fma((z - t), ((y - x) / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x - y), Float64(Float64(z - a) / t), y)
	tmp = 0.0
	if (t <= -0.0011)
		tmp = t_1;
	elseif (t <= 1.9e-48)
		tmp = fma(Float64(z - t), Float64(Float64(y - x) / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t, -0.0011], t$95$1, If[LessEqual[t, 1.9e-48], N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -0.00110000000000000007 or 1.90000000000000001e-48 < t

   1. Initial program 52.0%

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 78.8%

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

   if -0.00110000000000000007 < t < 1.90000000000000001e-48

   1. Initial program 90.5%

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

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 82.9

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

   5. Applied rewrites 82.9%

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

Alternative 12: 74.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x - y, \frac{z - a}{t}, y\right)\\ \mathbf{if}\;t \leq -0.00041:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-39}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- x y) (/ (- z a) t) y)))
   (if (<= t -0.00041) t_1 (if (<= t 1.2e-39) (+ x (* (- y x) (/ z a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x - y), ((z - a) / t), y);
	double tmp;
	if (t <= -0.00041) {
		tmp = t_1;
	} else if (t <= 1.2e-39) {
		tmp = x + ((y - x) * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x - y), Float64(Float64(z - a) / t), y)
	tmp = 0.0
	if (t <= -0.00041)
		tmp = t_1;
	elseif (t <= 1.2e-39)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t, -0.00041], t$95$1, If[LessEqual[t, 1.2e-39], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.0999999999999999e-4 or 1.20000000000000008e-39 < 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 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. distribute-rgt-out-- N/A

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 79.0%

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

   if -4.0999999999999999e-4 < t < 1.20000000000000008e-39

   1. Initial program 90.7%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 75.9

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

   5. Applied rewrites 75.9%

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

   7. Applied rewrites 82.0%

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

Alternative 13: 74.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x - y}{t}, z - a, y\right)\\ \mathbf{if}\;t \leq -0.00041:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-39}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- x y) t) (- z a) y)))
   (if (<= t -0.00041) t_1 (if (<= t 1.2e-39) (+ x (* (- y x) (/ z 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 <= -0.00041) {
		tmp = t_1;
	} else if (t <= 1.2e-39) {
		tmp = x + ((y - x) * (z / 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 <= -0.00041)
		tmp = t_1;
	elseif (t <= 1.2e-39)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / 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, -0.00041], t$95$1, If[LessEqual[t, 1.2e-39], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.0999999999999999e-4 or 1.20000000000000008e-39 < 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 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. distribute-rgt-out-- N/A

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 79.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 77.3%

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

   if -4.0999999999999999e-4 < t < 1.20000000000000008e-39

   1. Initial program 90.7%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 75.9

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

   5. Applied rewrites 75.9%

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

   7. Applied rewrites 82.0%

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

Alternative 14: 28.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - x\right)\\ \mathbf{if}\;t \leq -112000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-293}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- y x))))
   (if (<= t -112000000.0)
     t_1
     (if (<= t 2.1e-293) (/ (* y z) a) (if (<= t 3e-72) (* z (/ x z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y - x);
	double tmp;
	if (t <= -112000000.0) {
		tmp = t_1;
	} else if (t <= 2.1e-293) {
		tmp = (y * z) / a;
	} else if (t <= 3e-72) {
		tmp = z * (x / z);
	} 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)
    if (t <= (-112000000.0d0)) then
        tmp = t_1
    else if (t <= 2.1d-293) then
        tmp = (y * z) / a
    else if (t <= 3d-72) then
        tmp = z * (x / z)
    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);
	double tmp;
	if (t <= -112000000.0) {
		tmp = t_1;
	} else if (t <= 2.1e-293) {
		tmp = (y * z) / a;
	} else if (t <= 3e-72) {
		tmp = z * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y - x)
	tmp = 0
	if t <= -112000000.0:
		tmp = t_1
	elif t <= 2.1e-293:
		tmp = (y * z) / a
	elif t <= 3e-72:
		tmp = z * (x / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y - x))
	tmp = 0.0
	if (t <= -112000000.0)
		tmp = t_1;
	elseif (t <= 2.1e-293)
		tmp = Float64(Float64(y * z) / a);
	elseif (t <= 3e-72)
		tmp = Float64(z * Float64(x / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y - x);
	tmp = 0.0;
	if (t <= -112000000.0)
		tmp = t_1;
	elseif (t <= 2.1e-293)
		tmp = (y * z) / a;
	elseif (t <= 3e-72)
		tmp = z * (x / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -112000000.0], t$95$1, If[LessEqual[t, 2.1e-293], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 3e-72], N[(z * N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.12e8 or 3e-72 < t

   1. Initial program 52.7%

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

   3. Taylor expanded in t around inf

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

      1. lower--.f64 29.7

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

   5. Applied rewrites 29.7%

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

   if -1.12e8 < t < 2.10000000000000005e-293

   1. Initial program 88.8%

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

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 79.2

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

   5. Applied rewrites 79.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 53.5%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 39.3%

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

   if 2.10000000000000005e-293 < t < 3e-72

   1. Initial program 92.2%

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

   3. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. associate-+r+ N/A

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

      3. associate-+l+ N/A

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

   5. Applied rewrites 90.1%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 35.3%

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

Alternative 15: 70.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x - y, \frac{z}{t}, y\right)\\ \mathbf{if}\;t \leq -0.096:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-39}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- x y) (/ z t) y)))
   (if (<= t -0.096) t_1 (if (<= t 1.2e-39) (+ x (* (- y x) (/ z a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x - y), (z / t), y);
	double tmp;
	if (t <= -0.096) {
		tmp = t_1;
	} else if (t <= 1.2e-39) {
		tmp = x + ((y - x) * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x - y), Float64(z / t), y)
	tmp = 0.0
	if (t <= -0.096)
		tmp = t_1;
	elseif (t <= 1.2e-39)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(z / t), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t, -0.096], t$95$1, If[LessEqual[t, 1.2e-39], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -0.096000000000000002 or 1.20000000000000008e-39 < 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 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. distribute-rgt-out-- N/A

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 79.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 68.0%

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

   if -0.096000000000000002 < t < 1.20000000000000008e-39

   1. Initial program 90.7%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 75.9

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

   5. Applied rewrites 75.9%

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

   7. Applied rewrites 82.0%

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

Alternative 16: 69.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x - y, \frac{z}{t}, y\right)\\ \mathbf{if}\;t \leq -0.06:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- x y) (/ z t) y)))
   (if (<= t -0.06) t_1 (if (<= t 1.2e-39) (fma z (/ (- y x) a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x - y), (z / t), y);
	double tmp;
	if (t <= -0.06) {
		tmp = t_1;
	} else if (t <= 1.2e-39) {
		tmp = fma(z, ((y - x) / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x - y), Float64(z / t), y)
	tmp = 0.0
	if (t <= -0.06)
		tmp = t_1;
	elseif (t <= 1.2e-39)
		tmp = fma(z, Float64(Float64(y - x) / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(z / t), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t, -0.06], t$95$1, If[LessEqual[t, 1.2e-39], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -0.059999999999999998 or 1.20000000000000008e-39 < 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 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. distribute-rgt-out-- N/A

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 79.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 68.0%

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

   if -0.059999999999999998 < t < 1.20000000000000008e-39

   1. Initial program 90.7%

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

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 81.7

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

   5. Applied rewrites 81.7%

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

Alternative 17: 56.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{z}\\ \mathbf{if}\;t \leq -7 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y z))))
   (if (<= t -7e+144) t_1 (if (<= t 2.4e+111) (fma z (/ (- y x) a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / z);
	double tmp;
	if (t <= -7e+144) {
		tmp = t_1;
	} else if (t <= 2.4e+111) {
		tmp = fma(z, ((y - x) / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / z))
	tmp = 0.0
	if (t <= -7e+144)
		tmp = t_1;
	elseif (t <= 2.4e+111)
		tmp = fma(z, Float64(Float64(y - x) / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e+144], t$95$1, If[LessEqual[t, 2.4e+111], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.9999999999999996e144 or 2.40000000000000006e111 < t

   1. Initial program 43.0%

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

   3. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. associate-+r+ N/A

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

      3. associate-+l+ N/A

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

   5. Applied rewrites 64.9%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 40.9%

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

   if -6.9999999999999996e144 < t < 2.40000000000000006e111

   1. Initial program 82.6%

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

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 66.8

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

   5. Applied rewrites 66.8%

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

Alternative 18: 35.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+47}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-30}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.7e+47)
   (* z (/ y z))
   (if (<= t 1.02e-30) (fma t (/ x a) x) (+ x (- y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.7e+47) {
		tmp = z * (y / z);
	} else if (t <= 1.02e-30) {
		tmp = fma(t, (x / a), x);
	} else {
		tmp = x + (y - x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.7e+47)
		tmp = Float64(z * Float64(y / z));
	elseif (t <= 1.02e-30)
		tmp = fma(t, Float64(x / a), x);
	else
		tmp = Float64(x + Float64(y - x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.7e+47], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e-30], N[(t * N[(x / a), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(y - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6999999999999999e47

   1. Initial program 48.6%

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

   3. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. associate-+r+ N/A

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

      3. associate-+l+ N/A

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

   5. Applied rewrites 73.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 37.8%

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

   if -1.6999999999999999e47 < t < 1.0199999999999999e-30

   1. Initial program 88.5%

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

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 78.6

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

   5. Applied rewrites 78.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 54.9%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 38.9%

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

   if 1.0199999999999999e-30 < t

   1. Initial program 50.8%

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

   3. Taylor expanded in t around inf

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

      1. lower--.f64 28.9

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

   5. Applied rewrites 28.9%

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

Alternative 19: 27.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{z}\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+91}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y z))))
   (if (<= t -3.5e+142) t_1 (if (<= t 5.4e+91) (/ (* y z) a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / z);
	double tmp;
	if (t <= -3.5e+142) {
		tmp = t_1;
	} else if (t <= 5.4e+91) {
		tmp = (y * z) / a;
	} 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 * (y / z)
    if (t <= (-3.5d+142)) then
        tmp = t_1
    else if (t <= 5.4d+91) then
        tmp = (y * z) / a
    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 * (y / z);
	double tmp;
	if (t <= -3.5e+142) {
		tmp = t_1;
	} else if (t <= 5.4e+91) {
		tmp = (y * z) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / z)
	tmp = 0
	if t <= -3.5e+142:
		tmp = t_1
	elif t <= 5.4e+91:
		tmp = (y * z) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / z))
	tmp = 0.0
	if (t <= -3.5e+142)
		tmp = t_1;
	elseif (t <= 5.4e+91)
		tmp = Float64(Float64(y * z) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / z);
	tmp = 0.0;
	if (t <= -3.5e+142)
		tmp = t_1;
	elseif (t <= 5.4e+91)
		tmp = (y * z) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e+142], t$95$1, If[LessEqual[t, 5.4e+91], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.49999999999999997e142 or 5.4e91 < t

   1. Initial program 44.5%

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

   3. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. associate-+r+ N/A

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

      3. associate-+l+ N/A

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

   5. Applied rewrites 64.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 40.3%

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

   if -3.49999999999999997e142 < t < 5.4e91

   1. Initial program 82.8%

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

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 69.6

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

   5. Applied rewrites 69.6%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 40.5%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 27.8%

       \[\leadsto \frac{y \cdot z}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 28.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - x\right)\\ \mathbf{if}\;t \leq -112000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- y x))))
   (if (<= t -112000000.0) t_1 (if (<= t 7.5e+46) (/ (* y z) a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y - x);
	double tmp;
	if (t <= -112000000.0) {
		tmp = t_1;
	} else if (t <= 7.5e+46) {
		tmp = (y * z) / a;
	} 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)
    if (t <= (-112000000.0d0)) then
        tmp = t_1
    else if (t <= 7.5d+46) then
        tmp = (y * z) / a
    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);
	double tmp;
	if (t <= -112000000.0) {
		tmp = t_1;
	} else if (t <= 7.5e+46) {
		tmp = (y * z) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y - x)
	tmp = 0
	if t <= -112000000.0:
		tmp = t_1
	elif t <= 7.5e+46:
		tmp = (y * z) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y - x))
	tmp = 0.0
	if (t <= -112000000.0)
		tmp = t_1;
	elseif (t <= 7.5e+46)
		tmp = Float64(Float64(y * z) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y - x);
	tmp = 0.0;
	if (t <= -112000000.0)
		tmp = t_1;
	elseif (t <= 7.5e+46)
		tmp = (y * z) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -112000000.0], t$95$1, If[LessEqual[t, 7.5e+46], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.12e8 or 7.5000000000000003e46 < t

   1. Initial program 46.7%

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

   3. Taylor expanded in t around inf

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

      1. lower--.f64 32.0

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

   5. Applied rewrites 32.0%

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

   if -1.12e8 < t < 7.5000000000000003e46

   1. Initial program 87.8%

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

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 75.2

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

   5. Applied rewrites 75.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 44.9%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 30.6%

       \[\leadsto \frac{y \cdot z}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 19.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.15 \cdot 10^{+118}:\\ \;\;\;\;x + \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x 1.15e+118) (+ x (- y x)) (/ (* x t) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 1.15e+118) {
		tmp = x + (y - x);
	} else {
		tmp = (x * t) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= 1.15d+118) then
        tmp = x + (y - x)
    else
        tmp = (x * t) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 1.15e+118) {
		tmp = x + (y - x);
	} else {
		tmp = (x * t) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= 1.15e+118:
		tmp = x + (y - x)
	else:
		tmp = (x * t) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= 1.15e+118)
		tmp = Float64(x + Float64(y - x));
	else
		tmp = Float64(Float64(x * t) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= 1.15e+118)
		tmp = x + (y - x);
	else
		tmp = (x * t) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, 1.15e+118], N[(x + N[(y - x), $MachinePrecision]), $MachinePrecision], N[(N[(x * t), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.15000000000000008e118

   1. Initial program 71.4%

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

   3. Taylor expanded in t around inf

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

      1. lower--.f64 21.8

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

   5. Applied rewrites 21.8%

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

   if 1.15000000000000008e118 < x

   1. Initial program 54.5%

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

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 58.3

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

   5. Applied rewrites 58.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 19.3%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 21.9%

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

Alternative 22: 19.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.15 \cdot 10^{+118}:\\ \;\;\;\;x + \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x 1.15e+118) (+ x (- y x)) (* x (/ t a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 1.15e+118) {
		tmp = x + (y - x);
	} else {
		tmp = x * (t / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= 1.15d+118) then
        tmp = x + (y - x)
    else
        tmp = x * (t / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 1.15e+118) {
		tmp = x + (y - x);
	} else {
		tmp = x * (t / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= 1.15e+118:
		tmp = x + (y - x)
	else:
		tmp = x * (t / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= 1.15e+118)
		tmp = Float64(x + Float64(y - x));
	else
		tmp = Float64(x * Float64(t / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= 1.15e+118)
		tmp = x + (y - x);
	else
		tmp = x * (t / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, 1.15e+118], N[(x + N[(y - x), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.15000000000000008e118

   1. Initial program 71.4%

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

   3. Taylor expanded in t around inf

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

      1. lower--.f64 21.8

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

   5. Applied rewrites 21.8%

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

   if 1.15000000000000008e118 < x

   1. Initial program 54.5%

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

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 58.3

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

   5. Applied rewrites 58.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 19.3%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 21.9%

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

   13. Applied rewrites 19.6%

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

4. Final simplification 21.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.15 \cdot 10^{+118}:\\ \;\;\;\;x + \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 19.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.06 \cdot 10^{+118}:\\ \;\;\;\;x + \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x 1.06e+118) (+ x (- y x)) (* t (/ x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 1.06e+118) {
		tmp = x + (y - x);
	} else {
		tmp = t * (x / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= 1.06d+118) then
        tmp = x + (y - x)
    else
        tmp = t * (x / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 1.06e+118) {
		tmp = x + (y - x);
	} else {
		tmp = t * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= 1.06e+118:
		tmp = x + (y - x)
	else:
		tmp = t * (x / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= 1.06e+118)
		tmp = Float64(x + Float64(y - x));
	else
		tmp = Float64(t * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= 1.06e+118)
		tmp = x + (y - x);
	else
		tmp = t * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, 1.06e+118], N[(x + N[(y - x), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.06e118

   1. Initial program 71.4%

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

   3. Taylor expanded in t around inf

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

      1. lower--.f64 21.8

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

   5. Applied rewrites 21.8%

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

   if 1.06e118 < x

   1. Initial program 54.5%

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

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 58.3

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

   5. Applied rewrites 58.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 19.3%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 21.9%

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

   13. Applied rewrites 19.5%

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

Alternative 24: 19.2% accurate, 4.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.7%

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

3. Taylor expanded in t around inf

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

   1. lower--.f64 19.5

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

5. Applied rewrites 19.5%

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

Alternative 25: 2.8% accurate, 4.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.7%

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

3. Taylor expanded in t around inf

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

   1. lower--.f64 19.5

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

5. Applied rewrites 19.5%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 2.8%

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

Developer Target 1: 86.7% 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 2024222 
(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))))