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

Percentage Accurate: 68.7% → 88.5%

Time: 11.5s

Alternatives: 19

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.7% 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: 88.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{t}\\ t_2 := \left(z - a\right) \cdot t\_1\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+155}:\\ \;\;\;\;\mathsf{fma}\left(t\_2, \frac{a}{t}, t\_2\right) + y\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+259}:\\ \;\;\;\;\frac{y - x}{\frac{a - t}{z - t}} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, z - a, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x y) t)) (t_2 (* (- z a) t_1)))
   (if (<= t -3.8e+155)
     (+ (fma t_2 (/ a t) t_2) y)
     (if (<= t 7.5e+259)
       (+ (/ (- y x) (/ (- a t) (- z t))) x)
       (fma t_1 (- z a) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) / t;
	double t_2 = (z - a) * t_1;
	double tmp;
	if (t <= -3.8e+155) {
		tmp = fma(t_2, (a / t), t_2) + y;
	} else if (t <= 7.5e+259) {
		tmp = ((y - x) / ((a - t) / (z - t))) + x;
	} else {
		tmp = fma(t_1, (z - a), y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) / t)
	t_2 = Float64(Float64(z - a) * t_1)
	tmp = 0.0
	if (t <= -3.8e+155)
		tmp = Float64(fma(t_2, Float64(a / t), t_2) + y);
	elseif (t <= 7.5e+259)
		tmp = Float64(Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))) + x);
	else
		tmp = fma(t_1, Float64(z - a), y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z - a), $MachinePrecision] * t$95$1), $MachinePrecision]}, If[LessEqual[t, -3.8e+155], N[(N[(t$95$2 * N[(a / t), $MachinePrecision] + t$95$2), $MachinePrecision] + y), $MachinePrecision], If[LessEqual[t, 7.5e+259], N[(N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(t$95$1 * N[(z - a), $MachinePrecision] + y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.8000000000000001e155

   1. Initial program 14.7%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\left(y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right)\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]

   5. Applied rewrites 93.1%

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

   if -3.8000000000000001e155 < t < 7.4999999999999995e259

   1. Initial program 79.5%

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

      1. lift-/.f64 N/A

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

      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 91.3

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

   4. Applied rewrites 91.3%

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

   if 7.4999999999999995e259 < t

   1. Initial program 10.4%

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

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 99.9%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+155}:\\ \;\;\;\;\mathsf{fma}\left(\left(z - a\right) \cdot \frac{x - y}{t}, \frac{a}{t}, \left(z - a\right) \cdot \frac{x - y}{t}\right) + y\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+259}:\\ \;\;\;\;\frac{y - x}{\frac{a - t}{z - t}} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, z - a, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 81.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{\frac{t}{x - y}}, z - a, y\right)\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-131}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t} + x\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-6}:\\ \;\;\;\;\frac{y - x}{\frac{a - t}{z}} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, z - a, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.6e+104)
   (fma (/ 1.0 (/ t (- x y))) (- z a) y)
   (if (<= t -7.4e-131)
     (+ (/ (* (- z t) (- y x)) (- a t)) x)
     (if (<= t 1.4e-6)
       (+ (/ (- y x) (/ (- a t) z)) x)
       (fma (/ (- x y) t) (- z a) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.6e+104) {
		tmp = fma((1.0 / (t / (x - y))), (z - a), y);
	} else if (t <= -7.4e-131) {
		tmp = (((z - t) * (y - x)) / (a - t)) + x;
	} else if (t <= 1.4e-6) {
		tmp = ((y - x) / ((a - t) / z)) + x;
	} else {
		tmp = fma(((x - y) / t), (z - a), y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.6e+104)
		tmp = fma(Float64(1.0 / Float64(t / Float64(x - y))), Float64(z - a), y);
	elseif (t <= -7.4e-131)
		tmp = Float64(Float64(Float64(Float64(z - t) * Float64(y - x)) / Float64(a - t)) + x);
	elseif (t <= 1.4e-6)
		tmp = Float64(Float64(Float64(y - x) / Float64(Float64(a - t) / z)) + x);
	else
		tmp = fma(Float64(Float64(x - y) / t), Float64(z - a), y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.6e+104], N[(N[(1.0 / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(z - a), $MachinePrecision] + y), $MachinePrecision], If[LessEqual[t, -7.4e-131], N[(N[(N[(N[(z - t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 1.4e-6], N[(N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.59999999999999938e104

   1. Initial program 24.7%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 88.1%

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

   7. Applied rewrites 88.2%

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

   if -7.59999999999999938e104 < t < -7.4000000000000004e-131

   1. Initial program 85.3%

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

   if -7.4000000000000004e-131 < t < 1.39999999999999994e-6

   1. Initial program 91.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 96.9

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

   7. Applied rewrites 96.9%

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

   if 1.39999999999999994e-6 < t

   1. Initial program 42.8%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 77.6%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{\frac{t}{x - y}}, z - a, y\right)\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-131}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t} + x\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-6}:\\ \;\;\;\;\frac{y - x}{\frac{a - t}{z}} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, z - a, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x - y}{t}, z - a, y\right)\\ \mathbf{if}\;t \leq -7.6 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-131}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t} + x\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-6}:\\ \;\;\;\;\frac{y - x}{\frac{a - t}{z}} + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- x y) t) (- z a) y)))
   (if (<= t -7.6e+104)
     t_1
     (if (<= t -7.4e-131)
       (+ (/ (* (- z t) (- y x)) (- a t)) x)
       (if (<= t 1.4e-6) (+ (/ (- y x) (/ (- a t) z)) x) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((x - y) / t), (z - a), y);
	double tmp;
	if (t <= -7.6e+104) {
		tmp = t_1;
	} else if (t <= -7.4e-131) {
		tmp = (((z - t) * (y - x)) / (a - t)) + x;
	} else if (t <= 1.4e-6) {
		tmp = ((y - x) / ((a - t) / z)) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(x - y) / t), Float64(z - a), y)
	tmp = 0.0
	if (t <= -7.6e+104)
		tmp = t_1;
	elseif (t <= -7.4e-131)
		tmp = Float64(Float64(Float64(Float64(z - t) * Float64(y - x)) / Float64(a - t)) + x);
	elseif (t <= 1.4e-6)
		tmp = Float64(Float64(Float64(y - x) / Float64(Float64(a - t) / z)) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t, -7.6e+104], t$95$1, If[LessEqual[t, -7.4e-131], N[(N[(N[(N[(z - t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 1.4e-6], N[(N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.59999999999999938e104 or 1.39999999999999994e-6 < t

   1. Initial program 35.8%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 81.7%

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

   if -7.59999999999999938e104 < t < -7.4000000000000004e-131

   1. Initial program 85.3%

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

   if -7.4000000000000004e-131 < t < 1.39999999999999994e-6

   1. Initial program 91.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 96.9

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

   7. Applied rewrites 96.9%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, z - a, y\right)\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-131}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t} + x\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-6}:\\ \;\;\;\;\frac{y - x}{\frac{a - t}{z}} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, z - a, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+155}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{\frac{t}{x - y}}, z - a, y\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+259}:\\ \;\;\;\;\frac{y - x}{\frac{a - t}{z - t}} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, z - a, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.9e+155)
   (fma (/ 1.0 (/ t (- x y))) (- z a) y)
   (if (<= t 7.5e+259)
     (+ (/ (- y x) (/ (- a t) (- z t))) x)
     (fma (/ (- x y) t) (- z a) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.9e+155) {
		tmp = fma((1.0 / (t / (x - y))), (z - a), y);
	} else if (t <= 7.5e+259) {
		tmp = ((y - x) / ((a - t) / (z - t))) + x;
	} else {
		tmp = fma(((x - y) / t), (z - a), y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.9e+155)
		tmp = fma(Float64(1.0 / Float64(t / Float64(x - y))), Float64(z - a), y);
	elseif (t <= 7.5e+259)
		tmp = Float64(Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))) + x);
	else
		tmp = fma(Float64(Float64(x - y) / t), Float64(z - a), y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.9e+155], N[(N[(1.0 / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(z - a), $MachinePrecision] + y), $MachinePrecision], If[LessEqual[t, 7.5e+259], N[(N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.8999999999999999e155

   1. Initial program 14.7%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 91.3%

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

   7. Applied rewrites 91.4%

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

   if -2.8999999999999999e155 < t < 7.4999999999999995e259

   1. Initial program 79.5%

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

      1. lift-/.f64 N/A

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

      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 91.3

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

   4. Applied rewrites 91.3%

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

   if 7.4999999999999995e259 < t

   1. Initial program 10.4%

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

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 99.9%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+155}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{\frac{t}{x - y}}, z - a, y\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+259}:\\ \;\;\;\;\frac{y - x}{\frac{a - t}{z - t}} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, z - a, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x - y}{t}, z - a, y\right)\\ \mathbf{if}\;t \leq -7.6 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{+18}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t} + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- x y) t) (- z a) y)))
   (if (<= t -7.6e+104)
     t_1
     (if (<= t 7.4e+18) (+ (/ (* (- z t) (- y x)) (- a t)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((x - y) / t), (z - a), y);
	double tmp;
	if (t <= -7.6e+104) {
		tmp = t_1;
	} else if (t <= 7.4e+18) {
		tmp = (((z - t) * (y - x)) / (a - t)) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(x - y) / t), Float64(z - a), y)
	tmp = 0.0
	if (t <= -7.6e+104)
		tmp = t_1;
	elseif (t <= 7.4e+18)
		tmp = Float64(Float64(Float64(Float64(z - t) * Float64(y - x)) / Float64(a - t)) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t, -7.6e+104], t$95$1, If[LessEqual[t, 7.4e+18], N[(N[(N[(N[(z - t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.59999999999999938e104 or 7.4e18 < t

   1. Initial program 34.1%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 82.1%

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

   if -7.59999999999999938e104 < t < 7.4e18

   1. Initial program 89.0%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, z - a, y\right)\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{+18}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, z - a, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 44.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{y - x}{t}, y\right)\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-96}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot z}{t}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-29}:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8e+18)
   (fma a (/ (- y x) t) y)
   (if (<= t -2.9e-96)
     (/ (* (- x y) z) t)
     (if (<= t 1.9e-29) (* (/ z (- a t)) y) (fma (/ x t) z y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8e+18) {
		tmp = fma(a, ((y - x) / t), y);
	} else if (t <= -2.9e-96) {
		tmp = ((x - y) * z) / t;
	} else if (t <= 1.9e-29) {
		tmp = (z / (a - t)) * y;
	} else {
		tmp = fma((x / t), z, y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8e+18)
		tmp = fma(a, Float64(Float64(y - x) / t), y);
	elseif (t <= -2.9e-96)
		tmp = Float64(Float64(Float64(x - y) * z) / t);
	elseif (t <= 1.9e-29)
		tmp = Float64(Float64(z / Float64(a - t)) * y);
	else
		tmp = fma(Float64(x / t), z, y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8e+18], N[(a * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] + y), $MachinePrecision], If[LessEqual[t, -2.9e-96], N[(N[(N[(x - y), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 1.9e-29], N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(N[(x / t), $MachinePrecision] * z + y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8e18

   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 t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 81.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 61.6%

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

   if -8e18 < t < -2.89999999999999994e-96

   1. Initial program 85.8%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 50.7%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 2.3%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 49.5%

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

   if -2.89999999999999994e-96 < t < 1.89999999999999988e-29

   1. Initial program 92.3%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 40.3

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

   5. Applied rewrites 40.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 37.4%

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

   if 1.89999999999999988e-29 < t

   1. Initial program 47.1%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 74.9%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 64.4%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 55.7%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{y - x}{t}, y\right)\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-96}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot z}{t}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-29}:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 47.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{t}, z, y\right)\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-96}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot z}{t}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-29}:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ x t) z y)))
   (if (<= t -1.7e+17)
     t_1
     (if (<= t -2.9e-96)
       (/ (* (- x y) z) t)
       (if (<= t 1.9e-29) (* (/ z (- a t)) y) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x / t), z, y);
	double tmp;
	if (t <= -1.7e+17) {
		tmp = t_1;
	} else if (t <= -2.9e-96) {
		tmp = ((x - y) * z) / t;
	} else if (t <= 1.9e-29) {
		tmp = (z / (a - t)) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x / t), z, y)
	tmp = 0.0
	if (t <= -1.7e+17)
		tmp = t_1;
	elseif (t <= -2.9e-96)
		tmp = Float64(Float64(Float64(x - y) * z) / t);
	elseif (t <= 1.9e-29)
		tmp = Float64(Float64(z / Float64(a - t)) * y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] * z + y), $MachinePrecision]}, If[LessEqual[t, -1.7e+17], t$95$1, If[LessEqual[t, -2.9e-96], N[(N[(N[(x - y), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 1.9e-29], N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.7e17 or 1.89999999999999988e-29 < t

   1. Initial program 44.0%

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

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 77.9%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 64.2%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 55.6%

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

   if -1.7e17 < t < -2.89999999999999994e-96

   1. Initial program 85.8%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 50.7%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 2.3%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 49.5%

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

   if -2.89999999999999994e-96 < t < 1.89999999999999988e-29

   1. Initial program 92.3%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 40.3

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

   5. Applied rewrites 40.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 37.4%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+17}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z, y\right)\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-96}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot z}{t}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-29}:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{t}, z, y\right)\\ \mathbf{if}\;t \leq -8 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-96}:\\ \;\;\;\;\frac{x - y}{t} \cdot z\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-29}:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ x t) z y)))
   (if (<= t -8e+18)
     t_1
     (if (<= t -3e-96)
       (* (/ (- x y) t) z)
       (if (<= t 1.9e-29) (* (/ z (- a t)) y) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x / t), z, y);
	double tmp;
	if (t <= -8e+18) {
		tmp = t_1;
	} else if (t <= -3e-96) {
		tmp = ((x - y) / t) * z;
	} else if (t <= 1.9e-29) {
		tmp = (z / (a - t)) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x / t), z, y)
	tmp = 0.0
	if (t <= -8e+18)
		tmp = t_1;
	elseif (t <= -3e-96)
		tmp = Float64(Float64(Float64(x - y) / t) * z);
	elseif (t <= 1.9e-29)
		tmp = Float64(Float64(z / Float64(a - t)) * y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] * z + y), $MachinePrecision]}, If[LessEqual[t, -8e+18], t$95$1, If[LessEqual[t, -3e-96], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t, 1.9e-29], N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8e18 or 1.89999999999999988e-29 < t

   1. Initial program 44.0%

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

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 77.9%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 64.2%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 55.6%

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

   if -8e18 < t < -3e-96

   1. Initial program 85.8%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 50.7%

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

   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 46.7%

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

   if -3e-96 < t < 1.89999999999999988e-29

   1. Initial program 92.3%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 40.3

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

   5. Applied rewrites 40.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 37.4%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z, y\right)\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-96}:\\ \;\;\;\;\frac{x - y}{t} \cdot z\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-29}:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - x, \frac{z - t}{a}, x\right)\\ \mathbf{if}\;a \leq -2 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, z - a, y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y x) (/ (- z t) a) x)))
   (if (<= a -2e+18)
     t_1
     (if (<= a 2.05e+74) (fma (/ (- x y) t) (- z a) y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - x), ((z - t) / a), x);
	double tmp;
	if (a <= -2e+18) {
		tmp = t_1;
	} else if (a <= 2.05e+74) {
		tmp = fma(((x - y) / t), (z - a), y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - x), Float64(Float64(z - t) / a), x)
	tmp = 0.0
	if (a <= -2e+18)
		tmp = t_1;
	elseif (a <= 2.05e+74)
		tmp = fma(Float64(Float64(x - y) / t), Float64(z - a), y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -2e+18], t$95$1, If[LessEqual[a, 2.05e+74], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2e18 or 2.05e74 < a

   1. Initial program 68.3%

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

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

      5. lift--.f64 N/A

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

      6. flip-- N/A

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

      7. clear-num N/A

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

      8. un-div-inv N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. clear-num N/A

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

      12. flip-- N/A

          \[\leadsto x + \frac{\frac{z - t}{a - t}}{\frac{1}{\color{blue}{y - x}}} \]

      13. lift--.f64 N/A

          \[\leadsto x + \frac{\frac{z - t}{a - t}}{\frac{1}{\color{blue}{y - x}}} \]

      14. lower-/.f64 92.2

          \[\leadsto x + \frac{\frac{z - t}{a - t}}{\color{blue}{\frac{1}{y - x}}} \]

   4. Applied rewrites 92.2%

      \[\leadsto x + \color{blue}{\frac{\frac{z - t}{a - t}}{\frac{1}{y - x}}} \]

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 84.7

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

   7. Applied rewrites 84.7%

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

   if -2e18 < a < 2.05e74

   1. Initial program 68.5%

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

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 82.1%

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

Alternative 10: 70.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y - x}{a}, z, x\right)\\ \mathbf{if}\;a \leq -8.8 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+95}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, z - a, y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- y x) a) z x)))
   (if (<= a -8.8e+24)
     t_1
     (if (<= a 5.6e+95) (fma (/ (- x y) t) (- z a) y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((y - x) / a), z, x);
	double tmp;
	if (a <= -8.8e+24) {
		tmp = t_1;
	} else if (a <= 5.6e+95) {
		tmp = fma(((x - y) / t), (z - a), y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(y - x) / a), z, x)
	tmp = 0.0
	if (a <= -8.8e+24)
		tmp = t_1;
	elseif (a <= 5.6e+95)
		tmp = fma(Float64(Float64(x - y) / t), Float64(z - a), y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[a, -8.8e+24], t$95$1, If[LessEqual[a, 5.6e+95], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -8.80000000000000007e24 or 5.5999999999999995e95 < a

   1. Initial program 69.4%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 78.7

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

   5. Applied rewrites 78.7%

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

   if -8.80000000000000007e24 < a < 5.5999999999999995e95

   1. Initial program 67.8%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 80.0%

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

Alternative 11: 25.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t} \cdot x\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-293}:\\ \;\;\;\;\left(y - x\right) + x\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+91}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ z t) x)))
   (if (<= x -1.65e+31)
     t_1
     (if (<= x -2.1e-293)
       (+ (- y x) x)
       (if (<= x 1.15e+91) (/ (* z y) a) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z / t) * x;
	double tmp;
	if (x <= -1.65e+31) {
		tmp = t_1;
	} else if (x <= -2.1e-293) {
		tmp = (y - x) + x;
	} else if (x <= 1.15e+91) {
		tmp = (z * y) / 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 / t) * x
    if (x <= (-1.65d+31)) then
        tmp = t_1
    else if (x <= (-2.1d-293)) then
        tmp = (y - x) + x
    else if (x <= 1.15d+91) then
        tmp = (z * y) / 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 / t) * x;
	double tmp;
	if (x <= -1.65e+31) {
		tmp = t_1;
	} else if (x <= -2.1e-293) {
		tmp = (y - x) + x;
	} else if (x <= 1.15e+91) {
		tmp = (z * y) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z / t) * x
	tmp = 0
	if x <= -1.65e+31:
		tmp = t_1
	elif x <= -2.1e-293:
		tmp = (y - x) + x
	elif x <= 1.15e+91:
		tmp = (z * y) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z / t) * x)
	tmp = 0.0
	if (x <= -1.65e+31)
		tmp = t_1;
	elseif (x <= -2.1e-293)
		tmp = Float64(Float64(y - x) + x);
	elseif (x <= 1.15e+91)
		tmp = Float64(Float64(z * y) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z / t) * x;
	tmp = 0.0;
	if (x <= -1.65e+31)
		tmp = t_1;
	elseif (x <= -2.1e-293)
		tmp = (y - x) + x;
	elseif (x <= 1.15e+91)
		tmp = (z * y) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.65e+31], t$95$1, If[LessEqual[x, -2.1e-293], N[(N[(y - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[x, 1.15e+91], N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.64999999999999996e31 or 1.14999999999999996e91 < x

   1. Initial program 53.2%

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

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 55.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 42.9%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 31.1%

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

   if -1.64999999999999996e31 < x < -2.10000000000000005e-293

   1. Initial program 80.6%

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

   3. Taylor expanded in t around inf

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

      1. lower--.f64 29.5

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

   5. Applied rewrites 29.5%

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

   if -2.10000000000000005e-293 < x < 1.14999999999999996e91

   1. Initial program 77.6%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 66.1

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

   5. Applied rewrites 66.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 26.6%

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

4. Final simplification 29.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+31}:\\ \;\;\;\;\frac{z}{t} \cdot x\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-293}:\\ \;\;\;\;\left(y - x\right) + x\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+91}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y - x}{a}, z, x\right)\\ \mathbf{if}\;a \leq -1.75 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+77}:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{z}{t}, y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- y x) a) z x)))
   (if (<= a -1.75e+16) t_1 (if (<= a 2e+77) (fma (- x y) (/ z t) y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((y - x) / a), z, x);
	double tmp;
	if (a <= -1.75e+16) {
		tmp = t_1;
	} else if (a <= 2e+77) {
		tmp = fma((x - y), (z / t), y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(y - x) / a), z, x)
	tmp = 0.0
	if (a <= -1.75e+16)
		tmp = t_1;
	elseif (a <= 2e+77)
		tmp = fma(Float64(x - y), Float64(z / t), y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[a, -1.75e+16], t$95$1, If[LessEqual[a, 2e+77], N[(N[(x - y), $MachinePrecision] * N[(z / t), $MachinePrecision] + y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.75e16 or 1.99999999999999997e77 < a

   1. Initial program 67.1%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 74.8

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

   5. Applied rewrites 74.8%

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

   if -1.75e16 < a < 1.99999999999999997e77

   1. Initial program 69.4%

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

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 81.8%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 76.3%

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

   10. Applied rewrites 77.0%

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

Alternative 13: 52.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{z}{t}, y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) (- z t))))
   (if (<= a -2.1e+102) t_1 (if (<= a 7.2e+76) (fma (- x y) (/ z t) y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * (z - t);
	double tmp;
	if (a <= -2.1e+102) {
		tmp = t_1;
	} else if (a <= 7.2e+76) {
		tmp = fma((x - y), (z / t), y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * Float64(z - t))
	tmp = 0.0
	if (a <= -2.1e+102)
		tmp = t_1;
	elseif (a <= 7.2e+76)
		tmp = fma(Float64(x - y), Float64(z / t), y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.1e+102], t$95$1, If[LessEqual[a, 7.2e+76], N[(N[(x - y), $MachinePrecision] * N[(z / t), $MachinePrecision] + y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.10000000000000001e102 or 7.2000000000000006e76 < a

   1. Initial program 66.1%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 33.7

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

   5. Applied rewrites 33.7%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 27.1%

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

   if -2.10000000000000001e102 < a < 7.2000000000000006e76

   1. Initial program 69.8%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 78.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 72.7%

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

   10. Applied rewrites 73.3%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+102}:\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{z}{t}, y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 47.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{t}, z, y\right)\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{-70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-29}:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ x t) z y)))
   (if (<= t -2.5e-70) t_1 (if (<= t 1.9e-29) (* (/ z (- a t)) y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x / t), z, y);
	double tmp;
	if (t <= -2.5e-70) {
		tmp = t_1;
	} else if (t <= 1.9e-29) {
		tmp = (z / (a - t)) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x / t), z, y)
	tmp = 0.0
	if (t <= -2.5e-70)
		tmp = t_1;
	elseif (t <= 1.9e-29)
		tmp = Float64(Float64(z / Float64(a - t)) * y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] * z + y), $MachinePrecision]}, If[LessEqual[t, -2.5e-70], t$95$1, If[LessEqual[t, 1.9e-29], N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.4999999999999999e-70 or 1.89999999999999988e-29 < t

   1. Initial program 49.6%

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

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 73.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 61.9%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 51.6%

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

   if -2.4999999999999999e-70 < t < 1.89999999999999988e-29

   1. Initial program 93.0%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 41.9

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

   5. Applied rewrites 41.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 37.6%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-70}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z, y\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-29}:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 44.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{t}, z, y\right)\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{-90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-29}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ x t) z y)))
   (if (<= t -6.8e-90) t_1 (if (<= t 1.6e-29) (* (/ y a) z) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x / t), z, y);
	double tmp;
	if (t <= -6.8e-90) {
		tmp = t_1;
	} else if (t <= 1.6e-29) {
		tmp = (y / a) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x / t), z, y)
	tmp = 0.0
	if (t <= -6.8e-90)
		tmp = t_1;
	elseif (t <= 1.6e-29)
		tmp = Float64(Float64(y / a) * z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] * z + y), $MachinePrecision]}, If[LessEqual[t, -6.8e-90], t$95$1, If[LessEqual[t, 1.6e-29], N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.79999999999999988e-90 or 1.6e-29 < t

   1. Initial program 52.2%

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

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 72.7%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 61.9%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 49.9%

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

   if -6.79999999999999988e-90 < t < 1.6e-29

   1. Initial program 92.5%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 40.2

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

   5. Applied rewrites 40.2%

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

   7. Applied rewrites 40.7%

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

   8. Taylor expanded in a around inf

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

   10. Applied rewrites 35.2%

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

   11. Taylor expanded in t around 0

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

   13. Applied rewrites 32.7%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{-90}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z, y\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-29}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, z, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 27.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -43000000000:\\ \;\;\;\;\frac{z}{t} \cdot x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+51}:\\ \;\;\;\;\left(y - x\right) + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -43000000000.0)
   (* (/ z t) x)
   (if (<= z 6.6e+51) (+ (- y x) x) (* (/ y a) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -43000000000.0) {
		tmp = (z / t) * x;
	} else if (z <= 6.6e+51) {
		tmp = (y - x) + x;
	} else {
		tmp = (y / a) * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-43000000000.0d0)) then
        tmp = (z / t) * x
    else if (z <= 6.6d+51) then
        tmp = (y - x) + x
    else
        tmp = (y / a) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -43000000000.0) {
		tmp = (z / t) * x;
	} else if (z <= 6.6e+51) {
		tmp = (y - x) + x;
	} else {
		tmp = (y / a) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -43000000000.0:
		tmp = (z / t) * x
	elif z <= 6.6e+51:
		tmp = (y - x) + x
	else:
		tmp = (y / a) * z
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -43000000000.0)
		tmp = Float64(Float64(z / t) * x);
	elseif (z <= 6.6e+51)
		tmp = Float64(Float64(y - x) + x);
	else
		tmp = Float64(Float64(y / a) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -43000000000.0)
		tmp = (z / t) * x;
	elseif (z <= 6.6e+51)
		tmp = (y - x) + x;
	else
		tmp = (y / a) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -43000000000.0], N[(N[(z / t), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 6.6e+51], N[(N[(y - x), $MachinePrecision] + x), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.3e10

   1. Initial program 64.1%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 66.8%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 63.4%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 33.7%

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

   if -4.3e10 < z < 6.5999999999999994e51

   1. Initial program 72.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 23.0

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

   5. Applied rewrites 23.0%

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

   if 6.5999999999999994e51 < z

   1. Initial program 63.3%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 55.9

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

   5. Applied rewrites 55.9%

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

   7. Applied rewrites 56.0%

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

   8. Taylor expanded in a around inf

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

   10. Applied rewrites 40.9%

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

   11. Taylor expanded in t around 0

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

   13. Applied rewrites 39.9%

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

4. Final simplification 29.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -43000000000:\\ \;\;\;\;\frac{z}{t} \cdot x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+51}:\\ \;\;\;\;\left(y - x\right) + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 28.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) + x\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (- y x) x)))
   (if (<= t -1.7e+17) t_1 (if (<= t 6.5e-8) (/ (* z y) a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - x) + x;
	double tmp;
	if (t <= -1.7e+17) {
		tmp = t_1;
	} else if (t <= 6.5e-8) {
		tmp = (z * y) / 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 = (y - x) + x
    if (t <= (-1.7d+17)) then
        tmp = t_1
    else if (t <= 6.5d-8) then
        tmp = (z * y) / 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 = (y - x) + x;
	double tmp;
	if (t <= -1.7e+17) {
		tmp = t_1;
	} else if (t <= 6.5e-8) {
		tmp = (z * y) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - x) + x
	tmp = 0
	if t <= -1.7e+17:
		tmp = t_1
	elif t <= 6.5e-8:
		tmp = (z * y) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - x) + x)
	tmp = 0.0
	if (t <= -1.7e+17)
		tmp = t_1;
	elseif (t <= 6.5e-8)
		tmp = Float64(Float64(z * y) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - x) + x;
	tmp = 0.0;
	if (t <= -1.7e+17)
		tmp = t_1;
	elseif (t <= 6.5e-8)
		tmp = (z * y) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -1.7e+17], t$95$1, If[LessEqual[t, 6.5e-8], N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.7e17 or 6.49999999999999997e-8 < t

   1. Initial program 41.6%

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

   3. Taylor expanded in t around inf

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

      1. lower--.f64 29.5

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

   5. Applied rewrites 29.5%

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

   if -1.7e17 < t < 6.49999999999999997e-8

   1. Initial program 91.0%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 41.0

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

   5. Applied rewrites 41.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 24.8%

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

4. Final simplification 27.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+17}:\\ \;\;\;\;\left(y - x\right) + x\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 19.4% accurate, 4.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.4%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
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 16.5

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

5. Applied rewrites 16.5%

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

6. Final simplification 16.5%

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

Alternative 19: 2.8% accurate, 4.8× speedup

Math

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

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(Float64(-x) + 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 68.4%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
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 16.5

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

5. Applied rewrites 16.5%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 2.7%

   \[\leadsto x + \left(-x\right) \]

9. Final simplification 2.7%

   \[\leadsto \left(-x\right) + x \]
10. 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 2024243 
(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))))