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

Percentage Accurate: 67.9% → 88.7%

Time: 9.6s

Alternatives: 22

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.9% 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: 88.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-275}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{z - a}{t}, y\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+275}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- z t) (/ (- y x) (- a t)) x))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 -2e-275)
     t_1
     (if (<= t_2 0.0)
       (fma (- x y) (/ (- z a) t) y)
       (if (<= t_2 2e+275) t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((z - t), ((y - x) / (a - t)), x);
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -2e-275) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = fma((x - y), ((z - a) / t), y);
	} else if (t_2 <= 2e+275) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(z - t), Float64(Float64(y - x) / Float64(a - t)), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -2e-275)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = fma(Float64(x - y), Float64(Float64(z - a) / t), y);
	elseif (t_2 <= 2e+275)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-275], t$95$1, If[LessEqual[t$95$2, 0.0], N[(N[(x - y), $MachinePrecision] * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] + y), $MachinePrecision], If[LessEqual[t$95$2, 2e+275], t$95$2, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.99999999999999987e-275 or 1.99999999999999992e275 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 60.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 85.4

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

   4. Applied rewrites 85.4%

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

   if -1.99999999999999987e-275 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.5%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 99.7%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 1.99999999999999992e275

   1. Initial program 94.3%

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

Alternative 2: 90.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-275} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\mathsf{fma}\left(\frac{y - x}{t} \cdot \left(z - a\right), a, \left(z - a\right) \cdot \left(y - x\right)\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -2e-275) (not (<= t_1 0.0)))
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (- y (/ (fma (* (/ (- y x) t) (- z a)) a (* (- z a) (- y x))) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -2e-275) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y - (fma((((y - x) / t) * (z - a)), a, ((z - a) * (y - x))) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -2e-275) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(y - Float64(fma(Float64(Float64(Float64(y - x) / t) * Float64(z - a)), a, Float64(Float64(z - a) * Float64(y - x))) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-275], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(N[(N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision] * a + N[(N[(z - a), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.99999999999999987e-275 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 71.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 88.0

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

   4. Applied rewrites 88.0%

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

   if -1.99999999999999987e-275 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.5%

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

   3. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 99.8%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-275} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\mathsf{fma}\left(\frac{y - x}{t} \cdot \left(z - a\right), a, \left(z - a\right) \cdot \left(y - x\right)\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-275} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{z - a}{t}, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -2e-275) (not (<= t_1 0.0)))
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (fma (- x y) (/ (- z a) t) y))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -2e-275) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = fma((x - y), ((z - a) / t), y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -2e-275) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = fma(Float64(x - y), Float64(Float64(z - a) / t), y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-275], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.99999999999999987e-275 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 71.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 88.0

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

   4. Applied rewrites 88.0%

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

   if -1.99999999999999987e-275 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.5%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 99.7%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-275} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{z - a}{t}, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-275} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{z - a}{t}, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -2e-275) (not (<= t_1 0.0)))
     (fma (- z t) (/ (- y x) (- a t)) x)
     (fma (- x y) (/ (- z a) t) y))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -2e-275) || !(t_1 <= 0.0)) {
		tmp = fma((z - t), ((y - x) / (a - t)), x);
	} else {
		tmp = fma((x - y), ((z - a) / t), y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -2e-275) || !(t_1 <= 0.0))
		tmp = fma(Float64(z - t), Float64(Float64(y - x) / Float64(a - t)), x);
	else
		tmp = fma(Float64(x - y), Float64(Float64(z - a) / t), y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-275], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.99999999999999987e-275 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 71.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 84.1

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

   4. Applied rewrites 84.1%

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

   if -1.99999999999999987e-275 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.5%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 99.7%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-275} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{z - a}{t}, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{t}{a - t}, x\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-113}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, z, y\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z (- a t)))))
   (if (<= a -6.5e+78)
     (fma (- x y) (/ t (- a t)) x)
     (if (<= a -3e-28)
       t_1
       (if (<= a 7e-113)
         (fma (/ (- x y) t) z y)
         (if (<= a 3.9e+95) t_1 (fma (- y x) (/ z a) x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - x) * (z / (a - t));
	double tmp;
	if (a <= -6.5e+78) {
		tmp = fma((x - y), (t / (a - t)), x);
	} else if (a <= -3e-28) {
		tmp = t_1;
	} else if (a <= 7e-113) {
		tmp = fma(((x - y) / t), z, y);
	} else if (a <= 3.9e+95) {
		tmp = t_1;
	} else {
		tmp = fma((y - x), (z / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - x) * Float64(z / Float64(a - t)))
	tmp = 0.0
	if (a <= -6.5e+78)
		tmp = fma(Float64(x - y), Float64(t / Float64(a - t)), x);
	elseif (a <= -3e-28)
		tmp = t_1;
	elseif (a <= 7e-113)
		tmp = fma(Float64(Float64(x - y) / t), z, y);
	elseif (a <= 3.9e+95)
		tmp = t_1;
	else
		tmp = fma(Float64(y - x), Float64(z / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.5e+78], N[(N[(x - y), $MachinePrecision] * N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, -3e-28], t$95$1, If[LessEqual[a, 7e-113], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * z + y), $MachinePrecision], If[LessEqual[a, 3.9e+95], t$95$1, N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision] + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.50000000000000036e78

   1. Initial program 68.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. unsub-neg N/A

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

      13. remove-double-neg N/A

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

      14. lower--.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 74.4

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

   5. Applied rewrites 74.4%

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

   if -6.50000000000000036e78 < a < -3.00000000000000003e-28 or 7.00000000000000057e-113 < a < 3.8999999999999997e95

   1. Initial program 69.6%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 64.4

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

   5. Applied rewrites 64.4%

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

   if -3.00000000000000003e-28 < a < 7.00000000000000057e-113

   1. Initial program 62.3%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 79.1%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 78.5%

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

   if 3.8999999999999997e95 < a

   1. Initial program 69.0%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 75.7

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

   5. Applied rewrites 75.7%

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

   7. Applied rewrites 77.7%

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

Alternative 6: 68.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - x, \frac{z}{a}, x\right)\\ \mathbf{if}\;a \leq -1.28 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-113}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, z, y\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+95}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y x) (/ z a) x)))
   (if (<= a -1.28e+29)
     t_1
     (if (<= a 7e-113)
       (fma (/ (- x y) t) z y)
       (if (<= a 3.9e+95) (* (- y x) (/ z (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - x), (z / a), x);
	double tmp;
	if (a <= -1.28e+29) {
		tmp = t_1;
	} else if (a <= 7e-113) {
		tmp = fma(((x - y) / t), z, y);
	} else if (a <= 3.9e+95) {
		tmp = (y - x) * (z / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - x), Float64(z / a), x)
	tmp = 0.0
	if (a <= -1.28e+29)
		tmp = t_1;
	elseif (a <= 7e-113)
		tmp = fma(Float64(Float64(x - y) / t), z, y);
	elseif (a <= 3.9e+95)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	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[(z / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -1.28e+29], t$95$1, If[LessEqual[a, 7e-113], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * z + y), $MachinePrecision], If[LessEqual[a, 3.9e+95], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.28e29 or 3.8999999999999997e95 < a

   1. Initial program 68.9%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 70.8

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

   5. Applied rewrites 70.8%

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

   7. Applied rewrites 73.4%

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

   if -1.28e29 < a < 7.00000000000000057e-113

   1. Initial program 63.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 76.5%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 74.7%

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

   if 7.00000000000000057e-113 < a < 3.8999999999999997e95

   1. Initial program 69.7%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 63.8

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

   5. Applied rewrites 63.8%

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

Alternative 7: 52.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{-27}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-112}:\\ \;\;\;\;\mathsf{fma}\left(-y, \frac{z}{t}, y\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+99}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.06e-27)
   (fma (/ y a) z x)
   (if (<= a 4.6e-112)
     (fma (- y) (/ z t) y)
     (if (<= a 1.15e+99) (/ (* (- y x) z) a) (- x (* x (/ z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.06e-27) {
		tmp = fma((y / a), z, x);
	} else if (a <= 4.6e-112) {
		tmp = fma(-y, (z / t), y);
	} else if (a <= 1.15e+99) {
		tmp = ((y - x) * z) / a;
	} else {
		tmp = x - (x * (z / a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.06e-27)
		tmp = fma(Float64(y / a), z, x);
	elseif (a <= 4.6e-112)
		tmp = fma(Float64(-y), Float64(z / t), y);
	elseif (a <= 1.15e+99)
		tmp = Float64(Float64(Float64(y - x) * z) / a);
	else
		tmp = Float64(x - Float64(x * Float64(z / a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.06e-27], N[(N[(y / a), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[a, 4.6e-112], N[((-y) * N[(z / t), $MachinePrecision] + y), $MachinePrecision], If[LessEqual[a, 1.15e+99], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.05999999999999998e-27

   1. Initial program 68.9%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 61.4

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

   5. Applied rewrites 61.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 55.1%

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

   if -1.05999999999999998e-27 < a < 4.59999999999999981e-112

   1. Initial program 62.3%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 79.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 78.3%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 52.4%

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

   if 4.59999999999999981e-112 < a < 1.1500000000000001e99

   1. Initial program 70.4%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 50.2

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

   5. Applied rewrites 50.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 45.6%

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

   if 1.1500000000000001e99 < a

   1. Initial program 68.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 77.1

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

   5. Applied rewrites 77.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 20.7%

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

   9. Taylor expanded in y around 0

      \[\leadsto x + \color{blue}{-1 \cdot \frac{x \cdot z}{a}} \]
   10. Step-by-step derivation

   11. Applied rewrites 68.8%

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

Alternative 8: 47.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{-53}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-113}:\\ \;\;\;\;\frac{x - y}{t} \cdot z\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+99}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.95e-53)
   (fma (/ y a) z x)
   (if (<= a 2.15e-113)
     (* (/ (- x y) t) z)
     (if (<= a 1.15e+99) (/ (* (- y x) z) a) (- x (* x (/ z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.95e-53) {
		tmp = fma((y / a), z, x);
	} else if (a <= 2.15e-113) {
		tmp = ((x - y) / t) * z;
	} else if (a <= 1.15e+99) {
		tmp = ((y - x) * z) / a;
	} else {
		tmp = x - (x * (z / a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.95e-53)
		tmp = fma(Float64(y / a), z, x);
	elseif (a <= 2.15e-113)
		tmp = Float64(Float64(Float64(x - y) / t) * z);
	elseif (a <= 1.15e+99)
		tmp = Float64(Float64(Float64(y - x) * z) / a);
	else
		tmp = Float64(x - Float64(x * Float64(z / a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.95e-53], N[(N[(y / a), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[a, 2.15e-113], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[a, 1.15e+99], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.9500000000000001e-53

   1. Initial program 68.9%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 59.4

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

   5. Applied rewrites 59.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 52.4%

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

   if -1.9500000000000001e-53 < a < 2.15e-113

   1. Initial program 61.9%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 79.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 43.8%

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

   if 2.15e-113 < a < 1.1500000000000001e99

   1. Initial program 70.4%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 50.2

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

   5. Applied rewrites 50.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 45.6%

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

   if 1.1500000000000001e99 < a

   1. Initial program 68.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 77.1

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

   5. Applied rewrites 77.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 20.7%

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

   9. Taylor expanded in y around 0

      \[\leadsto x + \color{blue}{-1 \cdot \frac{x \cdot z}{a}} \]
   10. Step-by-step derivation

   11. Applied rewrites 68.8%

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

Alternative 9: 47.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{-53}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-112}:\\ \;\;\;\;\frac{x - y}{t} \cdot z\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+99}:\\ \;\;\;\;\frac{z}{a} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.95e-53)
   (fma (/ y a) z x)
   (if (<= a 1.55e-112)
     (* (/ (- x y) t) z)
     (if (<= a 1.15e+99) (* (/ z a) (- y x)) (- x (* x (/ z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.95e-53) {
		tmp = fma((y / a), z, x);
	} else if (a <= 1.55e-112) {
		tmp = ((x - y) / t) * z;
	} else if (a <= 1.15e+99) {
		tmp = (z / a) * (y - x);
	} else {
		tmp = x - (x * (z / a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.95e-53)
		tmp = fma(Float64(y / a), z, x);
	elseif (a <= 1.55e-112)
		tmp = Float64(Float64(Float64(x - y) / t) * z);
	elseif (a <= 1.15e+99)
		tmp = Float64(Float64(z / a) * Float64(y - x));
	else
		tmp = Float64(x - Float64(x * Float64(z / a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.95e-53], N[(N[(y / a), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[a, 1.55e-112], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[a, 1.15e+99], N[(N[(z / a), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.9500000000000001e-53

   1. Initial program 68.9%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 59.4

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

   5. Applied rewrites 59.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 52.4%

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

   if -1.9500000000000001e-53 < a < 1.5499999999999999e-112

   1. Initial program 61.9%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 79.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 43.8%

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

   if 1.5499999999999999e-112 < a < 1.1500000000000001e99

   1. Initial program 70.4%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 50.2

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

   5. Applied rewrites 50.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 45.6%

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

   10. Applied rewrites 45.6%

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

   if 1.1500000000000001e99 < a

   1. Initial program 68.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 77.1

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

   5. Applied rewrites 77.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 20.7%

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

   9. Taylor expanded in y around 0

      \[\leadsto x + \color{blue}{-1 \cdot \frac{x \cdot z}{a}} \]
   10. Step-by-step derivation

   11. Applied rewrites 68.8%

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

Alternative 10: 47.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{-53}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-112}:\\ \;\;\;\;\frac{x - y}{t} \cdot z\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+99}:\\ \;\;\;\;\frac{z}{a} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{z}{a}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.95e-53)
   (fma (/ y a) z x)
   (if (<= a 1.55e-112)
     (* (/ (- x y) t) z)
     (if (<= a 1.15e+99) (* (/ z a) (- y x)) (* (- 1.0 (/ z a)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.95e-53) {
		tmp = fma((y / a), z, x);
	} else if (a <= 1.55e-112) {
		tmp = ((x - y) / t) * z;
	} else if (a <= 1.15e+99) {
		tmp = (z / a) * (y - x);
	} else {
		tmp = (1.0 - (z / a)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.95e-53)
		tmp = fma(Float64(y / a), z, x);
	elseif (a <= 1.55e-112)
		tmp = Float64(Float64(Float64(x - y) / t) * z);
	elseif (a <= 1.15e+99)
		tmp = Float64(Float64(z / a) * Float64(y - x));
	else
		tmp = Float64(Float64(1.0 - Float64(z / a)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.95e-53], N[(N[(y / a), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[a, 1.55e-112], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[a, 1.15e+99], N[(N[(z / a), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.9500000000000001e-53

   1. Initial program 68.9%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 59.4

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

   5. Applied rewrites 59.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 52.4%

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

   if -1.9500000000000001e-53 < a < 1.5499999999999999e-112

   1. Initial program 61.9%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 79.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 43.8%

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

   if 1.5499999999999999e-112 < a < 1.1500000000000001e99

   1. Initial program 70.4%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 50.2

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

   5. Applied rewrites 50.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 45.6%

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

   10. Applied rewrites 45.6%

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

   if 1.1500000000000001e99 < a

   1. Initial program 68.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 77.1

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

   5. Applied rewrites 77.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 68.8%

      \[\leadsto \left(1 - \frac{z}{a}\right) \cdot \color{blue}{x} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 11: 75.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+29} \lor \neg \left(a \leq 9.5 \cdot 10^{+19}\right):\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{z - a}{t}, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.7e+29) (not (<= a 9.5e+19)))
   (fma (- z t) (/ (- y x) a) x)
   (fma (- x y) (/ (- z a) t) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.7e+29) || !(a <= 9.5e+19)) {
		tmp = fma((z - t), ((y - x) / a), x);
	} else {
		tmp = fma((x - y), ((z - a) / t), y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.7e+29) || !(a <= 9.5e+19))
		tmp = fma(Float64(z - t), Float64(Float64(y - x) / a), x);
	else
		tmp = fma(Float64(x - y), Float64(Float64(z - a) / t), y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.7e+29], N[Not[LessEqual[a, 9.5e+19]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.7e29 or 9.5e19 < a

   1. Initial program 68.3%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 79.3

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

   5. Applied rewrites 79.3%

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

   if -2.7e29 < a < 9.5e19

   1. Initial program 65.0%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 73.1%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+29} \lor \neg \left(a \leq 9.5 \cdot 10^{+19}\right):\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{z - a}{t}, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a}, x\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{z - a}{t}, y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y - x}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.7e+29)
   (fma (- y x) (/ (- z t) a) x)
   (if (<= a 9.5e+19)
     (fma (- x y) (/ (- z a) t) y)
     (fma (- z t) (/ (- y x) a) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.7e+29) {
		tmp = fma((y - x), ((z - t) / a), x);
	} else if (a <= 9.5e+19) {
		tmp = fma((x - y), ((z - a) / t), y);
	} else {
		tmp = fma((z - t), ((y - x) / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.7e+29)
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / a), x);
	elseif (a <= 9.5e+19)
		tmp = fma(Float64(x - y), Float64(Float64(z - a) / t), y);
	else
		tmp = fma(Float64(z - t), Float64(Float64(y - x) / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.7e+29], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 9.5e+19], N[(N[(x - y), $MachinePrecision] * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] + y), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.7e29

   1. Initial program 68.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 96.5

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

   4. Applied rewrites 96.5%

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

   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 81.2

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

   7. Applied rewrites 81.2%

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

   if -2.7e29 < a < 9.5e19

   1. Initial program 65.0%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 73.1%

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

   if 9.5e19 < a

   1. Initial program 67.7%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 80.7

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

   5. Applied rewrites 80.7%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a}, x\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{z - a}{t}, y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y - x}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 71.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{t}{a - t}, x\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{z - a}{t}, y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.2e+78)
   (fma (- x y) (/ t (- a t)) x)
   (if (<= a 9.5e+19) (fma (- x y) (/ (- z a) t) y) (fma (- y x) (/ z a) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.2e+78) {
		tmp = fma((x - y), (t / (a - t)), x);
	} else if (a <= 9.5e+19) {
		tmp = fma((x - y), ((z - a) / t), y);
	} else {
		tmp = fma((y - x), (z / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.2e+78)
		tmp = fma(Float64(x - y), Float64(t / Float64(a - t)), x);
	elseif (a <= 9.5e+19)
		tmp = fma(Float64(x - y), Float64(Float64(z - a) / t), y);
	else
		tmp = fma(Float64(y - x), Float64(z / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.2e+78], N[(N[(x - y), $MachinePrecision] * N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 9.5e+19], N[(N[(x - y), $MachinePrecision] * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] + y), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.2000000000000002e78

   1. Initial program 68.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. unsub-neg N/A

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

      13. remove-double-neg N/A

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

      14. lower--.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 74.4

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

   5. Applied rewrites 74.4%

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

   if -4.2000000000000002e78 < a < 9.5e19

   1. Initial program 65.2%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 71.6%

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

   if 9.5e19 < a

   1. Initial program 67.7%

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

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 71.1

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

   5. Applied rewrites 71.1%

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

   7. Applied rewrites 72.7%

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

Alternative 14: 69.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.28 \cdot 10^{+29} \lor \neg \left(a \leq 9.2 \cdot 10^{+19}\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, z, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.28e+29) (not (<= a 9.2e+19)))
   (fma (- y x) (/ z a) x)
   (fma (/ (- x y) t) z y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.28e+29) || !(a <= 9.2e+19)) {
		tmp = fma((y - x), (z / a), x);
	} else {
		tmp = fma(((x - y) / t), z, y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.28e+29) || !(a <= 9.2e+19))
		tmp = fma(Float64(y - x), Float64(z / a), x);
	else
		tmp = fma(Float64(Float64(x - y) / t), z, y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.28e+29], N[Not[LessEqual[a, 9.2e+19]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * z + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.28e29 or 9.2e19 < a

   1. Initial program 68.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 69.0

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

   5. Applied rewrites 69.0%

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

   7. Applied rewrites 71.4%

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

   if -1.28e29 < a < 9.2e19

   1. Initial program 65.0%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 73.1%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 68.9%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.28 \cdot 10^{+29} \lor \neg \left(a \leq 9.2 \cdot 10^{+19}\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, z, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 64.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+30}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, z, y\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.55e+30)
   (fma (/ y a) z x)
   (if (<= a 2.1e+20) (fma (/ (- x y) t) z y) (- x (* x (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.55e+30) {
		tmp = fma((y / a), z, x);
	} else if (a <= 2.1e+20) {
		tmp = fma(((x - y) / t), z, y);
	} else {
		tmp = x - (x * (z / a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.55e+30)
		tmp = fma(Float64(y / a), z, x);
	elseif (a <= 2.1e+20)
		tmp = fma(Float64(Float64(x - y) / t), z, y);
	else
		tmp = Float64(x - Float64(x * Float64(z / a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.55e+30], N[(N[(y / a), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[a, 2.1e+20], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * z + y), $MachinePrecision], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.5499999999999999e30

   1. Initial program 68.9%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 66.8

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

   5. Applied rewrites 66.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 60.7%

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

   if -1.5499999999999999e30 < a < 2.1e20

   1. Initial program 65.0%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 73.1%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 68.9%

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

   if 2.1e20 < a

   1. Initial program 67.7%

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

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 71.1

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

   5. Applied rewrites 71.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 27.0%

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

   9. Taylor expanded in y around 0

      \[\leadsto x + \color{blue}{-1 \cdot \frac{x \cdot z}{a}} \]
   10. Step-by-step derivation

   11. Applied rewrites 58.8%

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

Alternative 16: 49.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{-53} \lor \neg \left(a \leq 7.2 \cdot 10^{-95}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.95e-53) (not (<= a 7.2e-95)))
   (fma (/ y a) z x)
   (* (/ (- x y) t) z)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.95e-53) || !(a <= 7.2e-95)) {
		tmp = fma((y / a), z, x);
	} else {
		tmp = ((x - y) / t) * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.95e-53) || !(a <= 7.2e-95))
		tmp = fma(Float64(y / a), z, x);
	else
		tmp = Float64(Float64(Float64(x - y) / t) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.95e-53], N[Not[LessEqual[a, 7.2e-95]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * z + x), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.9500000000000001e-53 or 7.2e-95 < 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. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 61.6

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 52.3%

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

   if -1.9500000000000001e-53 < a < 7.2e-95

   1. Initial program 63.4%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 78.7%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 44.1%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{-53} \lor \neg \left(a \leq 7.2 \cdot 10^{-95}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 49.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+156} \lor \neg \left(t \leq 3.35 \cdot 10^{-12}\right):\\ \;\;\;\;x + \left(-\left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4e+156) (not (<= t 3.35e-12)))
   (+ x (- (- y)))
   (fma (/ y a) z x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4e+156) || !(t <= 3.35e-12)) {
		tmp = x + -(-y);
	} else {
		tmp = fma((y / a), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4e+156) || !(t <= 3.35e-12))
		tmp = Float64(x + Float64(-Float64(-y)));
	else
		tmp = fma(Float64(y / a), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4e+156], N[Not[LessEqual[t, 3.35e-12]], $MachinePrecision]], N[(x + (-(-y))), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.9999999999999999e156 or 3.3500000000000001e-12 < t

   1. Initial program 39.7%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. distribute-rgt-in N/A

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

      5. mul-1-neg N/A

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

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

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

      7. *-commutative N/A

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

      8. div-sub N/A

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

   5. Applied rewrites 46.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 29.4%

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

   9. Taylor expanded in x around 0

      \[\leadsto x + \left(--1 \cdot y\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 37.2%

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

   if -3.9999999999999999e156 < t < 3.3500000000000001e-12

   1. Initial program 84.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 62.8

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

   5. Applied rewrites 62.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 50.2%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+156} \lor \neg \left(t \leq 3.35 \cdot 10^{-12}\right):\\ \;\;\;\;x + \left(-\left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 39.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+148} \lor \neg \left(z \leq 1.4 \cdot 10^{+41}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(-\left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.4e+148) (not (<= z 1.4e+41))) (* y (/ z a)) (+ x (- (- y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.4e+148) || !(z <= 1.4e+41)) {
		tmp = y * (z / a);
	} else {
		tmp = x + -(-y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.4d+148)) .or. (.not. (z <= 1.4d+41))) then
        tmp = y * (z / a)
    else
        tmp = x + -(-y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.4e+148) || !(z <= 1.4e+41)) {
		tmp = y * (z / a);
	} else {
		tmp = x + -(-y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.4e+148) or not (z <= 1.4e+41):
		tmp = y * (z / a)
	else:
		tmp = x + -(-y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.4e+148) || !(z <= 1.4e+41))
		tmp = Float64(y * Float64(z / a));
	else
		tmp = Float64(x + Float64(-Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.4e+148) || ~((z <= 1.4e+41)))
		tmp = y * (z / a);
	else
		tmp = x + -(-y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.4e+148], N[Not[LessEqual[z, 1.4e+41]], $MachinePrecision]], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], N[(x + (-(-y))), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3999999999999999e148 or 1.4e41 < z

   1. Initial program 68.7%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 78.6

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

   5. Applied rewrites 78.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 38.1%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 32.4%

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

   if -1.3999999999999999e148 < z < 1.4e41

   1. Initial program 65.4%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. distribute-rgt-in N/A

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

      5. mul-1-neg N/A

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

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

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

      7. *-commutative N/A

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

      8. div-sub N/A

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

   5. Applied rewrites 53.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 23.0%

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

   9. Taylor expanded in x around 0

      \[\leadsto x + \left(--1 \cdot y\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 42.0%

       \[\leadsto x + \left(-\left(-y\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+148} \lor \neg \left(z \leq 1.4 \cdot 10^{+41}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(-\left(-y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 38.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+149}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+41}:\\ \;\;\;\;x + \left(-\left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.9e+149)
   (/ (* z y) a)
   (if (<= z 1.4e+41) (+ x (- (- y))) (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+149) {
		tmp = (z * y) / a;
	} else if (z <= 1.4e+41) {
		tmp = x + -(-y);
	} else {
		tmp = y * (z / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.9d+149)) then
        tmp = (z * y) / a
    else if (z <= 1.4d+41) then
        tmp = x + -(-y)
    else
        tmp = y * (z / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+149) {
		tmp = (z * y) / a;
	} else if (z <= 1.4e+41) {
		tmp = x + -(-y);
	} else {
		tmp = y * (z / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.9e+149:
		tmp = (z * y) / a
	elif z <= 1.4e+41:
		tmp = x + -(-y)
	else:
		tmp = y * (z / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.9e+149)
		tmp = Float64(Float64(z * y) / a);
	elseif (z <= 1.4e+41)
		tmp = Float64(x + Float64(-Float64(-y)));
	else
		tmp = Float64(y * Float64(z / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.9e+149)
		tmp = (z * y) / a;
	elseif (z <= 1.4e+41)
		tmp = x + -(-y);
	else
		tmp = y * (z / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.9e+149], N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 1.4e+41], N[(x + (-(-y))), $MachinePrecision], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9e149

   1. Initial program 71.1%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 64.4

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

   5. Applied rewrites 64.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 40.0%

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

   if -1.9e149 < z < 1.4e41

   1. Initial program 65.4%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. distribute-rgt-in N/A

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

      5. mul-1-neg N/A

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

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

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

      7. *-commutative N/A

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

      8. div-sub N/A

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

   5. Applied rewrites 53.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 23.0%

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

   9. Taylor expanded in x around 0

      \[\leadsto x + \left(--1 \cdot y\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 42.0%

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

   if 1.4e41 < z

   1. Initial program 67.3%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 79.5

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

   5. Applied rewrites 79.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 33.6%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 29.7%

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

Alternative 20: 35.5% accurate, 3.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   1. associate--l+ N/A

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

   2. div-sub N/A

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

   3. +-commutative N/A

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

   4. distribute-rgt-in N/A

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

   5. mul-1-neg N/A

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

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

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

   7. *-commutative N/A

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

   8. div-sub N/A

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

5. Applied rewrites 66.0%

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

6. Taylor expanded in t around inf

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

8. Applied rewrites 17.5%

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

9. Taylor expanded in x around 0

   \[\leadsto x + \left(--1 \cdot y\right) \]
10. Step-by-step derivation

11. Applied rewrites 32.7%

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

Alternative 21: 19.7% accurate, 4.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 66.6%

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

3. Taylor expanded in z around inf

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

   1. associate--l+ N/A

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

   2. div-sub N/A

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

   3. +-commutative N/A

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

   4. distribute-rgt-in N/A

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

   5. mul-1-neg N/A

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

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

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

   7. *-commutative N/A

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

   8. div-sub N/A

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

5. Applied rewrites 66.0%

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

6. Taylor expanded in t around inf

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

8. Applied rewrites 17.5%

   \[\leadsto x + \left(-\left(x - y\right)\right) \]
9. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lower-+.f64 17.5

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

10. Applied rewrites 17.5%

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

Alternative 22: 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 66.6%

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

3. Taylor expanded in z around inf

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

   1. associate--l+ N/A

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

   2. div-sub N/A

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

   3. +-commutative N/A

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

   4. distribute-rgt-in N/A

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

   5. mul-1-neg N/A

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

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

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

   7. *-commutative N/A

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

   8. div-sub N/A

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

5. Applied rewrites 66.0%

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

6. Taylor expanded in t around inf

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

8. Applied rewrites 17.5%

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

9. Taylor expanded in x around inf

   \[\leadsto x + -1 \cdot x \]
10. Step-by-step derivation

11. Applied rewrites 2.9%

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

Developer Target 1: 87.1% 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 2024324 
(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))))