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

Percentage Accurate: 68.6% → 77.9%

Time: 9.0s

Alternatives: 15

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 77.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.000122 \lor \neg \left(a \leq 4.6 \cdot 10^{+31}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, \frac{t}{x} - 1, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-\left(t - x\right), \frac{y - a}{z}, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -0.000122) (not (<= a 4.6e+31)))
   (* (fma (/ (- y z) (- a z)) (- (/ t x) 1.0) 1.0) x)
   (fma (- (- t x)) (/ (- y a) z) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.000122) || !(a <= 4.6e+31)) {
		tmp = fma(((y - z) / (a - z)), ((t / x) - 1.0), 1.0) * x;
	} else {
		tmp = fma(-(t - x), ((y - a) / z), t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -0.000122) || !(a <= 4.6e+31))
		tmp = Float64(fma(Float64(Float64(y - z) / Float64(a - z)), Float64(Float64(t / x) - 1.0), 1.0) * x);
	else
		tmp = fma(Float64(-Float64(t - x)), Float64(Float64(y - a) / z), t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -0.000122], N[Not[LessEqual[a, 4.6e+31]], $MachinePrecision]], N[(N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(N[(t / x), $MachinePrecision] - 1.0), $MachinePrecision] + 1.0), $MachinePrecision] * x), $MachinePrecision], N[((-N[(t - x), $MachinePrecision]) * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.21999999999999997e-4 or 4.5999999999999999e31 < a

   1. Initial program 73.5%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 85.5%

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

   if -1.21999999999999997e-4 < a < 4.5999999999999999e31

   1. Initial program 56.9%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

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

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

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

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

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

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

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

      11. lower-*.f64 N/A

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

   5. Applied rewrites 66.1%

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

   6. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. div-sub N/A

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

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

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

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

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

      7. associate-*r/ N/A

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

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

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

      9. +-commutative N/A

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

   8. Applied rewrites 87.2%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.000122 \lor \neg \left(a \leq 4.6 \cdot 10^{+31}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, \frac{t}{x} - 1, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-\left(t - x\right), \frac{y - a}{z}, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 42.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+141}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{+49} \lor \neg \left(a \leq 3.1 \cdot 10^{+42}\right):\\ \;\;\;\;\frac{t - x}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.3e+141)
   (/ (* t (- y z)) a)
   (if (or (<= a -2.5e+49) (not (<= a 3.1e+42)))
     (* (/ (- t x) a) y)
     (fma (/ x z) y t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.3e+141) {
		tmp = (t * (y - z)) / a;
	} else if ((a <= -2.5e+49) || !(a <= 3.1e+42)) {
		tmp = ((t - x) / a) * y;
	} else {
		tmp = fma((x / z), y, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.3e+141)
		tmp = Float64(Float64(t * Float64(y - z)) / a);
	elseif ((a <= -2.5e+49) || !(a <= 3.1e+42))
		tmp = Float64(Float64(Float64(t - x) / a) * y);
	else
		tmp = fma(Float64(x / z), y, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.3e+141], N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[Or[LessEqual[a, -2.5e+49], N[Not[LessEqual[a, 3.1e+42]], $MachinePrecision]], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * y + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.3e141

   1. Initial program 80.4%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 83.0

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

   5. Applied rewrites 83.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 32.5%

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

   if -1.3e141 < a < -2.5000000000000002e49 or 3.1000000000000002e42 < a

   1. Initial program 68.2%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 84.1

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

   5. Applied rewrites 84.1%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 35.9%

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

   if -2.5000000000000002e49 < a < 3.1000000000000002e42

   1. Initial program 58.9%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

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

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

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

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

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

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

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

      11. lower-*.f64 N/A

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

   5. Applied rewrites 66.9%

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

   6. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. div-sub N/A

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

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

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

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

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

      7. associate-*r/ N/A

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

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

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

      9. +-commutative N/A

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

   8. Applied rewrites 85.1%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 82.4%

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

   12. Taylor expanded in x around inf

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

   14. Applied rewrites 71.3%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+141}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{+49} \lor \neg \left(a \leq 3.1 \cdot 10^{+42}\right):\\ \;\;\;\;\frac{t - x}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.000145 \lor \neg \left(a \leq 3 \cdot 10^{+32}\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-\left(t - x\right), \frac{y - a}{z}, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -0.000145) (not (<= a 3e+32)))
   (fma (- y z) (/ (- t x) a) x)
   (fma (- (- t x)) (/ (- y a) z) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.000145) || !(a <= 3e+32)) {
		tmp = fma((y - z), ((t - x) / a), x);
	} else {
		tmp = fma(-(t - x), ((y - a) / z), t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -0.000145) || !(a <= 3e+32))
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / a), x);
	else
		tmp = fma(Float64(-Float64(t - x)), Float64(Float64(y - a) / z), t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -0.000145], N[Not[LessEqual[a, 3e+32]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[((-N[(t - x), $MachinePrecision]) * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.45e-4 or 3e32 < a

   1. Initial program 73.5%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 83.2

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

   5. Applied rewrites 83.2%

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

   if -1.45e-4 < a < 3e32

   1. Initial program 56.9%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

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

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

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

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

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

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

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

      11. lower-*.f64 N/A

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

   5. Applied rewrites 66.1%

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

   6. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. div-sub N/A

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

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

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

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

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

      7. associate-*r/ N/A

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

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

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

      9. +-commutative N/A

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

   8. Applied rewrites 87.2%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.000145 \lor \neg \left(a \leq 3 \cdot 10^{+32}\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-\left(t - x\right), \frac{y - a}{z}, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.000122 \lor \neg \left(a \leq 2.6 \cdot 10^{+32}\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -0.000122) (not (<= a 2.6e+32)))
   (fma (- y z) (/ (- t x) a) x)
   (fma (/ (- x t) z) y t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.000122) || !(a <= 2.6e+32)) {
		tmp = fma((y - z), ((t - x) / a), x);
	} else {
		tmp = fma(((x - t) / z), y, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -0.000122) || !(a <= 2.6e+32))
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / a), x);
	else
		tmp = fma(Float64(Float64(x - t) / z), y, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -0.000122], N[Not[LessEqual[a, 2.6e+32]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.21999999999999997e-4 or 2.6000000000000002e32 < a

   1. Initial program 73.5%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 83.2

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

   5. Applied rewrites 83.2%

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

   if -1.21999999999999997e-4 < a < 2.6000000000000002e32

   1. Initial program 56.9%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

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

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

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

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

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

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

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

      11. lower-*.f64 N/A

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

   5. Applied rewrites 66.1%

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

   6. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. div-sub N/A

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

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

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

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

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

      7. associate-*r/ N/A

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

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

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

      9. +-commutative N/A

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

   8. Applied rewrites 87.2%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 84.3%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.000122 \lor \neg \left(a \leq 2.6 \cdot 10^{+32}\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.000202 \lor \neg \left(a \leq 1.35 \cdot 10^{+35}\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -0.000202) (not (<= a 1.35e+35)))
   (fma (- y z) (/ t a) x)
   (fma (/ (- x t) z) y t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.000202) || !(a <= 1.35e+35)) {
		tmp = fma((y - z), (t / a), x);
	} else {
		tmp = fma(((x - t) / z), y, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -0.000202) || !(a <= 1.35e+35))
		tmp = fma(Float64(y - z), Float64(t / a), x);
	else
		tmp = fma(Float64(Float64(x - t) / z), y, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -0.000202], N[Not[LessEqual[a, 1.35e+35]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.02000000000000004e-4 or 1.35000000000000001e35 < a

   1. Initial program 73.5%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 83.2

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

   5. Applied rewrites 83.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 72.8%

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

   if -2.02000000000000004e-4 < a < 1.35000000000000001e35

   1. Initial program 56.9%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

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

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

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

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

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

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

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

      11. lower-*.f64 N/A

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

   5. Applied rewrites 66.1%

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

   6. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. div-sub N/A

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

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

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

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

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

      7. associate-*r/ N/A

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

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

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

      9. +-commutative N/A

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

   8. Applied rewrites 87.2%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 84.3%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.000202 \lor \neg \left(a \leq 1.35 \cdot 10^{+35}\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.000202 \lor \neg \left(a \leq 1.5 \cdot 10^{+35}\right):\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -0.000202) (not (<= a 1.5e+35)))
   (+ x (/ (* t y) a))
   (fma (/ (- x t) z) y t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.000202) || !(a <= 1.5e+35)) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = fma(((x - t) / z), y, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -0.000202) || !(a <= 1.5e+35))
		tmp = Float64(x + Float64(Float64(t * y) / a));
	else
		tmp = fma(Float64(Float64(x - t) / z), y, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -0.000202], N[Not[LessEqual[a, 1.5e+35]], $MachinePrecision]], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.02000000000000004e-4 or 1.49999999999999995e35 < a

   1. Initial program 73.5%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 62.5

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

   5. Applied rewrites 62.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 58.5%

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

   if -2.02000000000000004e-4 < a < 1.49999999999999995e35

   1. Initial program 56.9%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

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

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

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

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

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

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

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

      11. lower-*.f64 N/A

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

   5. Applied rewrites 66.1%

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

   6. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. div-sub N/A

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

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

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

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

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

      7. associate-*r/ N/A

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

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

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

      9. +-commutative N/A

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

   8. Applied rewrites 87.2%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 84.3%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.000202 \lor \neg \left(a \leq 1.5 \cdot 10^{+35}\right):\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.000202:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t}{a}, x\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -0.000202)
   (fma (- y z) (/ t a) x)
   (if (<= a 2.6e+32) (fma (/ (- x t) z) y t) (fma (/ (- t x) a) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.000202) {
		tmp = fma((y - z), (t / a), x);
	} else if (a <= 2.6e+32) {
		tmp = fma(((x - t) / z), y, t);
	} else {
		tmp = fma(((t - x) / a), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -0.000202)
		tmp = fma(Float64(y - z), Float64(t / a), x);
	elseif (a <= 2.6e+32)
		tmp = fma(Float64(Float64(x - t) / z), y, t);
	else
		tmp = fma(Float64(Float64(t - x) / a), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -0.000202], N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 2.6e+32], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y + t), $MachinePrecision], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.02000000000000004e-4

   1. Initial program 78.6%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 83.2

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

   5. Applied rewrites 83.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 73.9%

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

   if -2.02000000000000004e-4 < a < 2.6000000000000002e32

   1. Initial program 56.9%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

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

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

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

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

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

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

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

      11. lower-*.f64 N/A

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

   5. Applied rewrites 66.1%

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

   6. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. div-sub N/A

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

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

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

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

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

      7. associate-*r/ N/A

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

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

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

      9. +-commutative N/A

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

   8. Applied rewrites 87.2%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 84.3%

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

   if 2.6000000000000002e32 < a

   1. Initial program 68.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 74.1

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

   5. Applied rewrites 74.1%

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

Alternative 8: 56.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.00019 \lor \neg \left(a \leq 1.5 \cdot 10^{+35}\right):\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -0.00019) (not (<= a 1.5e+35)))
   (+ x (/ (* t y) a))
   (fma (/ x z) y t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.00019) || !(a <= 1.5e+35)) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = fma((x / z), y, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -0.00019) || !(a <= 1.5e+35))
		tmp = Float64(x + Float64(Float64(t * y) / a));
	else
		tmp = fma(Float64(x / z), y, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -0.00019], N[Not[LessEqual[a, 1.5e+35]], $MachinePrecision]], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * y + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.9000000000000001e-4 or 1.49999999999999995e35 < a

   1. Initial program 73.5%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 62.5

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

   5. Applied rewrites 62.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 58.5%

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

   if -1.9000000000000001e-4 < a < 1.49999999999999995e35

   1. Initial program 56.9%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

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

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

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

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

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

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

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

      11. lower-*.f64 N/A

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

   5. Applied rewrites 66.1%

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

   6. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. div-sub N/A

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

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

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

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

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

      7. associate-*r/ N/A

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

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

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

      9. +-commutative N/A

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

   8. Applied rewrites 87.2%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 84.3%

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

   12. Taylor expanded in x around inf

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

   14. Applied rewrites 73.3%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00019 \lor \neg \left(a \leq 1.5 \cdot 10^{+35}\right):\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+22} \lor \neg \left(z \leq 2.5 \cdot 10^{-129}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.5e+22) (not (<= z 2.5e-129)))
   (fma (/ x z) y t)
   (* (- t x) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.5e+22) || !(z <= 2.5e-129)) {
		tmp = fma((x / z), y, t);
	} else {
		tmp = (t - x) * (y / a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.5e+22) || !(z <= 2.5e-129))
		tmp = fma(Float64(x / z), y, t);
	else
		tmp = Float64(Float64(t - x) * Float64(y / a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.5e+22], N[Not[LessEqual[z, 2.5e-129]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * y + t), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000021e22 or 2.50000000000000014e-129 < z

   1. Initial program 54.0%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

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

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

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

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

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

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

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

      11. lower-*.f64 N/A

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

   5. Applied rewrites 67.8%

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

   6. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. div-sub N/A

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

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

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

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

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

      7. associate-*r/ N/A

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

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

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

      9. +-commutative N/A

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

   8. Applied rewrites 68.9%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 64.9%

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

   12. Taylor expanded in x around inf

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

   14. Applied rewrites 58.1%

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

   if -5.50000000000000021e22 < z < 2.50000000000000014e-129

   1. Initial program 86.0%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 56.3

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

   5. Applied rewrites 56.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 46.8%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+22} \lor \neg \left(z \leq 2.5 \cdot 10^{-129}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+22} \lor \neg \left(z \leq 2.5 \cdot 10^{-129}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - x}{a} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.5e+22) (not (<= z 2.5e-129)))
   (fma (/ x z) y t)
   (* (/ (- t x) a) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.5e+22) || !(z <= 2.5e-129)) {
		tmp = fma((x / z), y, t);
	} else {
		tmp = ((t - x) / a) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.5e+22) || !(z <= 2.5e-129))
		tmp = fma(Float64(x / z), y, t);
	else
		tmp = Float64(Float64(Float64(t - x) / a) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.5e+22], N[Not[LessEqual[z, 2.5e-129]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * y + t), $MachinePrecision], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000021e22 or 2.50000000000000014e-129 < z

   1. Initial program 54.0%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

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

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

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

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

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

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

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

      11. lower-*.f64 N/A

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

   5. Applied rewrites 67.8%

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

   6. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. div-sub N/A

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

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

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

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

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

      7. associate-*r/ N/A

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

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

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

      9. +-commutative N/A

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

   8. Applied rewrites 68.9%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 64.9%

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

   12. Taylor expanded in x around inf

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

   14. Applied rewrites 58.1%

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

   if -5.50000000000000021e22 < z < 2.50000000000000014e-129

   1. Initial program 86.0%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 77.5

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

   5. Applied rewrites 77.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 42.5%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+22} \lor \neg \left(z \leq 2.5 \cdot 10^{-129}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - x}{a} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 26.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-38} \lor \neg \left(x \leq 1.9 \cdot 10^{+45}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.45e-38) (not (<= x 1.9e+45))) (* x (/ y z)) (+ x (- t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.45e-38) || !(x <= 1.9e+45)) {
		tmp = x * (y / z);
	} else {
		tmp = x + (t - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-1.45d-38)) .or. (.not. (x <= 1.9d+45))) then
        tmp = x * (y / z)
    else
        tmp = x + (t - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.45e-38) || !(x <= 1.9e+45)) {
		tmp = x * (y / z);
	} else {
		tmp = x + (t - x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.45e-38) or not (x <= 1.9e+45):
		tmp = x * (y / z)
	else:
		tmp = x + (t - x)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.45e-38) || !(x <= 1.9e+45))
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(x + Float64(t - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.45e-38) || ~((x <= 1.9e+45)))
		tmp = x * (y / z);
	else
		tmp = x + (t - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.45e-38], N[Not[LessEqual[x, 1.9e+45]], $MachinePrecision]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.44999999999999997e-38 or 1.9000000000000001e45 < x

   1. Initial program 54.7%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 34.1%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 47.1%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 28.9%

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

   if -1.44999999999999997e-38 < x < 1.9000000000000001e45

   1. Initial program 75.2%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 36.3

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

   5. Applied rewrites 36.3%

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

4. Final simplification 32.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-38} \lor \neg \left(x \leq 1.9 \cdot 10^{+45}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 40.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.9 \cdot 10^{+103}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x - t}{z} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 1.9e+103) (fma (/ x z) y t) (* (/ (- x t) z) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.9e+103) {
		tmp = fma((x / z), y, t);
	} else {
		tmp = ((x - t) / z) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 1.9e+103)
		tmp = fma(Float64(x / z), y, t);
	else
		tmp = Float64(Float64(Float64(x - t) / z) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 1.9e+103], N[(N[(x / z), $MachinePrecision] * y + t), $MachinePrecision], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.8999999999999998e103

   1. Initial program 64.6%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

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

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

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

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

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

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

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

      11. lower-*.f64 N/A

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

   5. Applied rewrites 72.3%

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

   6. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. div-sub N/A

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

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

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

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

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

      7. associate-*r/ N/A

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

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

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

      9. +-commutative N/A

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

   8. Applied rewrites 55.6%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 51.2%

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

   12. Taylor expanded in x around inf

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

   14. Applied rewrites 46.6%

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

   if 1.8999999999999998e103 < y

   1. Initial program 67.1%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

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

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

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

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

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

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

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

      11. lower-*.f64 N/A

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

   5. Applied rewrites 71.3%

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

   6. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. div-sub N/A

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

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

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

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

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

      7. associate-*r/ N/A

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

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

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

      9. +-commutative N/A

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

   8. Applied rewrites 46.7%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 44.2%

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

Alternative 13: 39.1% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 65.0%

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

3. Taylor expanded in t around inf

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

   1. associate--l+ N/A

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

   2. div-sub N/A

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

   3. +-commutative N/A

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

   4. *-lft-identity N/A

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

   5. metadata-eval N/A

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

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

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

   7. mul-1-neg N/A

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

   8. distribute-neg-in N/A

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

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

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

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

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

   11. lower-*.f64 N/A

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

5. Applied rewrites 72.1%

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

6. Taylor expanded in z around inf

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

   1. associate--l+ N/A

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

   2. associate-*r/ N/A

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

   3. associate-*r/ N/A

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

   4. div-sub N/A

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

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

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

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

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

   7. associate-*r/ N/A

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

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

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

   9. +-commutative N/A

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

8. Applied rewrites 54.0%

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

9. Taylor expanded in a around 0

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

11. Applied rewrites 51.1%

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

12. Taylor expanded in x around inf

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

14. Applied rewrites 44.5%

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

Alternative 14: 18.5% accurate, 4.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 65.0%

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

3. Taylor expanded in z around inf

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

   1. lower--.f64 22.2

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

5. Applied rewrites 22.2%

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

Alternative 15: 2.8% accurate, 4.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 65.0%

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

3. Taylor expanded in z around inf

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

   1. lower--.f64 22.2

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

5. Applied rewrites 22.2%

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

6. Taylor expanded in x around inf

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

8. Applied rewrites 2.7%

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

Developer Target 1: 83.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024329 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -125361310560950360000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- t (* (/ y z) (- t x))) (if (< z 44467023691138110000000000000000000000000000000000000000000000000) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x))))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))