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

Percentage Accurate: 68.3% → 88.6%

Time: 35.9s

Alternatives: 9

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x - y, \frac{z - a}{t}, y\right)\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+248}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- x y) (/ (- z a) t) y)))
   (if (<= t -2.5e+80)
     t_1
     (if (<= t 1.9e+248) (fma (/ (- z t) (- a t)) (- y x) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x - y), ((z - a) / t), y);
	double tmp;
	if (t <= -2.5e+80) {
		tmp = t_1;
	} else if (t <= 1.9e+248) {
		tmp = fma(((z - t) / (a - t)), (y - x), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x - y), Float64(Float64(z - a) / t), y)
	tmp = 0.0
	if (t <= -2.5e+80)
		tmp = t_1;
	elseif (t <= 1.9e+248)
		tmp = fma(Float64(Float64(z - t) / Float64(a - t)), Float64(y - x), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t, -2.5e+80], t$95$1, If[LessEqual[t, 1.9e+248], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.4999999999999998e80 or 1.9e248 < t

   1. Initial program 20.1%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 93.9%

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

   if -2.4999999999999998e80 < t < 1.9e248

   1. Initial program 79.4%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. remove-double-neg N/A

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

      5. lift--.f64 N/A

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

      6. remove-double-neg N/A

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

      7. lift-/.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-/.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-/.f64 90.6

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

   4. Applied rewrites 90.6%

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

Alternative 2: 76.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - x, \frac{z - t}{a}, x\right)\\ \mathbf{if}\;a \leq -3.7 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 28:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{z - a}{t}, y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y x) (/ (- z t) a) x)))
   (if (<= a -3.7e+22)
     t_1
     (if (<= a 28.0) (fma (- x y) (/ (- z a) t) y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - x), ((z - t) / a), x);
	double tmp;
	if (a <= -3.7e+22) {
		tmp = t_1;
	} else if (a <= 28.0) {
		tmp = fma((x - y), ((z - a) / t), y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - x), Float64(Float64(z - t) / a), x)
	tmp = 0.0
	if (a <= -3.7e+22)
		tmp = t_1;
	elseif (a <= 28.0)
		tmp = fma(Float64(x - y), Float64(Float64(z - a) / t), y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -3.7e+22], t$95$1, If[LessEqual[a, 28.0], N[(N[(x - y), $MachinePrecision] * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] + y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.6999999999999998e22 or 28 < a

   1. Initial program 70.5%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. *-commutative N/A

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

      4. lift--.f64 N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. un-div-inv N/A

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

      8. lower-/.f64 N/A

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

      9. clear-num N/A

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

      10. flip-- N/A

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

      11. lift--.f64 N/A

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

      12. lower-/.f64 70.4

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

   4. Applied rewrites 70.4%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 80.8

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

   7. Applied rewrites 80.8%

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

   if -3.6999999999999998e22 < a < 28

   1. Initial program 62.8%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 77.9%

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

Alternative 3: 72.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{if}\;a \leq -3.7 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 47:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{z - a}{t}, y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma z (/ (- y x) a) x)))
   (if (<= a -3.7e+22)
     t_1
     (if (<= a 47.0) (fma (- x y) (/ (- z a) t) y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(z, ((y - x) / a), x);
	double tmp;
	if (a <= -3.7e+22) {
		tmp = t_1;
	} else if (a <= 47.0) {
		tmp = fma((x - y), ((z - a) / t), y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(z, Float64(Float64(y - x) / a), x)
	tmp = 0.0
	if (a <= -3.7e+22)
		tmp = t_1;
	elseif (a <= 47.0)
		tmp = fma(Float64(x - y), Float64(Float64(z - a) / t), y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -3.7e+22], t$95$1, If[LessEqual[a, 47.0], N[(N[(x - y), $MachinePrecision] * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] + y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.6999999999999998e22 or 47 < a

   1. Initial program 70.5%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 72.9

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

   5. Applied rewrites 72.9%

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

   if -3.6999999999999998e22 < a < 47

   1. Initial program 62.8%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 77.9%

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

Alternative 4: 67.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-86}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma z (/ (- y x) a) x)))
   (if (<= a -9.5e-58) t_1 (if (<= a 1.4e-86) (+ y (/ (* z (- x y)) t)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(z, ((y - x) / a), x);
	double tmp;
	if (a <= -9.5e-58) {
		tmp = t_1;
	} else if (a <= 1.4e-86) {
		tmp = y + ((z * (x - y)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(z, Float64(Float64(y - x) / a), x)
	tmp = 0.0
	if (a <= -9.5e-58)
		tmp = t_1;
	elseif (a <= 1.4e-86)
		tmp = Float64(y + Float64(Float64(z * Float64(x - y)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -9.5e-58], t$95$1, If[LessEqual[a, 1.4e-86], N[(y + N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -9.4999999999999994e-58 or 1.40000000000000005e-86 < a

   1. Initial program 68.4%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 68.5

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

   5. Applied rewrites 68.5%

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

   if -9.4999999999999994e-58 < a < 1.40000000000000005e-86

   1. Initial program 63.8%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. distribute-lft-in N/A

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

      5. lift--.f64 N/A

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

      6. flip3-- N/A

         \[\leadsto x + \frac{\color{blue}{\frac{{y}^{3} - {x}^{3}}{y \cdot y + \left(x \cdot x + y \cdot x\right)}} \cdot \left(\mathsf{neg}\left(t\right)\right) + \left(y - x\right) \cdot z}{a - t} \]

      7. div-inv N/A

         \[\leadsto x + \frac{\color{blue}{\left(\left({y}^{3} - {x}^{3}\right) \cdot \frac{1}{y \cdot y + \left(x \cdot x + y \cdot x\right)}\right)} \cdot \left(\mathsf{neg}\left(t\right)\right) + \left(y - x\right) \cdot z}{a - t} \]

      8. associate-*l* N/A

         \[\leadsto x + \frac{\color{blue}{\left({y}^{3} - {x}^{3}\right) \cdot \left(\frac{1}{y \cdot y + \left(x \cdot x + y \cdot x\right)} \cdot \left(\mathsf{neg}\left(t\right)\right)\right)} + \left(y - x\right) \cdot z}{a - t} \]

      9. lower-fma.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\mathsf{fma}\left({y}^{3} - {x}^{3}, \frac{1}{y \cdot y + \left(x \cdot x + y \cdot x\right)} \cdot \left(\mathsf{neg}\left(t\right)\right), \left(y - x\right) \cdot z\right)}}{a - t} \]

   4. Applied rewrites 23.0%

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

   5. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 79.5

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

   7. Applied rewrites 79.5%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-58}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-86}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+134}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -2.3e+19) t_1 (if (<= t 2.7e+134) (fma z (/ (- y x) a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.3e+19) {
		tmp = t_1;
	} else if (t <= 2.7e+134) {
		tmp = fma(z, ((y - x) / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -2.3e+19)
		tmp = t_1;
	elseif (t <= 2.7e+134)
		tmp = fma(z, Float64(Float64(y - x) / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.3e+19], t$95$1, If[LessEqual[t, 2.7e+134], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.3e19 or 2.7e134 < t

   1. Initial program 33.0%

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

   3. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. div-sub N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

   5. Applied rewrites 71.6%

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

      1. lift--.f64 71.6

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

      2. remove-double-div N/A

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

      3. frac-2neg N/A

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

      4. metadata-eval N/A

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

      5. associate-/r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-neg.f64 71.6

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

   7. Applied rewrites 71.6%

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

   8. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. sub-neg N/A

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

      4. div-sub N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower--.f64 69.5

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

   10. Applied rewrites 69.5%

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

   if -2.3e19 < t < 2.7e134

   1. Initial program 83.6%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 69.0

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

   5. Applied rewrites 69.0%

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

Alternative 6: 59.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x - x\right)\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+134}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (- x x))))
   (if (<= t -1.8e+45) t_1 (if (<= t 2.7e+134) (fma z (/ (- y x) a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (x - x);
	double tmp;
	if (t <= -1.8e+45) {
		tmp = t_1;
	} else if (t <= 2.7e+134) {
		tmp = fma(z, ((y - x) / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(x - x))
	tmp = 0.0
	if (t <= -1.8e+45)
		tmp = t_1;
	elseif (t <= 2.7e+134)
		tmp = fma(z, Float64(Float64(y - x) / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(x - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.8e+45], t$95$1, If[LessEqual[t, 2.7e+134], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.8e45 or 2.7e134 < t

   1. Initial program 29.2%

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

   3. Taylor expanded in t around inf

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

      1. lower--.f64 31.0

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

   5. Applied rewrites 31.0%

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

      1. lift--.f64 N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 51.0

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

   7. Applied rewrites 51.0%

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

   if -1.8e45 < t < 2.7e134

   1. Initial program 83.7%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 67.9

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

   5. Applied rewrites 67.9%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+45}:\\ \;\;\;\;y + \left(x - x\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+134}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \left(x - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 25.9% accurate, 4.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 66.6%

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

3. Taylor expanded in t around inf

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

   1. lower--.f64 16.3

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

5. Applied rewrites 16.3%

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

   1. lift--.f64 N/A

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

   2. +-commutative N/A

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

   3. lift--.f64 N/A

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

   4. associate-+l- N/A

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

   5. lower--.f64 N/A

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

   6. lower--.f64 23.9

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

7. Applied rewrites 23.9%

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

8. Final simplification 23.9%

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

Alternative 8: 19.8% accurate, 4.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 66.6%

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

3. Taylor expanded in t around inf

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

   1. lower--.f64 16.3

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

5. Applied rewrites 16.3%

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

Alternative 9: 2.8% accurate, 29.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = 0.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 66.6%

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

3. Taylor expanded in t around inf

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

   1. lower--.f64 16.3

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

5. Applied rewrites 16.3%

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

6. Taylor expanded in y around 0

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

   1. mul-1-neg N/A

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

   2. lower-neg.f64 2.8

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

8. Applied rewrites 2.8%

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

   1. unsub-neg N/A

      \[\leadsto \color{blue}{x - x} \]

   2. +-inverses 2.8

      \[\leadsto \color{blue}{0} \]

10. Applied rewrites 2.8%

    \[\leadsto \color{blue}{0} \]
11. Add Preprocessing

Developer Target 1: 87.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024220 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< a -646122513817703/4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t)))) (if (< a 1887201585041587/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t)))))))

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