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

Percentage Accurate: 67.6% → 88.3%

Time: 10.7s

Alternatives: 17

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{z - y}{\frac{z - a}{x - t}}\\ t_2 := x - \frac{\left(z - y\right) \cdot \left(x - t\right)}{z - a}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-255}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t - \left(a - y\right) \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (- z y) (/ (- z a) (- x t)))))
        (t_2 (- x (/ (* (- z y) (- x t)) (- z a)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -1e-255)
       t_2
       (if (<= t_2 0.0) (- t (* (- a y) (/ (- x t) z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((z - y) / ((z - a) / (x - t)));
	double t_2 = x - (((z - y) * (x - t)) / (z - a));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -1e-255) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t - ((a - y) * ((x - t) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((z - y) / ((z - a) / (x - t)));
	double t_2 = x - (((z - y) * (x - t)) / (z - a));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -1e-255) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t - ((a - y) * ((x - t) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((z - y) / ((z - a) / (x - t)))
	t_2 = x - (((z - y) * (x - t)) / (z - a))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -1e-255:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t - ((a - y) * ((x - t) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(z - y) / Float64(Float64(z - a) / Float64(x - t))))
	t_2 = Float64(x - Float64(Float64(Float64(z - y) * Float64(x - t)) / Float64(z - a)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -1e-255)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t - Float64(Float64(a - y) * Float64(Float64(x - t) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((z - y) / ((z - a) / (x - t)));
	t_2 = x - (((z - y) * (x - t)) / (z - a));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -1e-255)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t - ((a - y) * ((x - t) / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(z - y), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(N[(z - y), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -1e-255], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t - N[(N[(a - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -inf.0 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 68.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 90.6

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

   4. Applied rewrites 90.6%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1e-255

   1. Initial program 97.2%

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

   if -1e-255 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 8.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 4.2

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

   4. Applied rewrites 4.2%

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

   5. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. lower--.f64 N/A

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

      7. div-sub N/A

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

      8. associate-/l* N/A

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

      9. associate-/l* N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 99.8

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

   7. Applied rewrites 99.8%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(z - y\right) \cdot \left(x - t\right)}{z - a} \leq -\infty:\\ \;\;\;\;x - \frac{z - y}{\frac{z - a}{x - t}}\\ \mathbf{elif}\;x - \frac{\left(z - y\right) \cdot \left(x - t\right)}{z - a} \leq -1 \cdot 10^{-255}:\\ \;\;\;\;x - \frac{\left(z - y\right) \cdot \left(x - t\right)}{z - a}\\ \mathbf{elif}\;x - \frac{\left(z - y\right) \cdot \left(x - t\right)}{z - a} \leq 0:\\ \;\;\;\;t - \left(a - y\right) \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - y}{\frac{z - a}{x - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 60.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \mathbf{if}\;a \leq -14600000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.45 \cdot 10^{-304}:\\ \;\;\;\;\left(\frac{y}{z} - 1\right) \cdot \left(-t\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-11}:\\ \;\;\;\;\frac{y}{z - a} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- t x) a) y x)))
   (if (<= a -14600000.0)
     t_1
     (if (<= a -3.45e-304)
       (* (- (/ y z) 1.0) (- t))
       (if (<= a 2.9e-11) (* (/ y (- z a)) (- x t)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((t - x) / a), y, x);
	double tmp;
	if (a <= -14600000.0) {
		tmp = t_1;
	} else if (a <= -3.45e-304) {
		tmp = ((y / z) - 1.0) * -t;
	} else if (a <= 2.9e-11) {
		tmp = (y / (z - a)) * (x - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(t - x) / a), y, x)
	tmp = 0.0
	if (a <= -14600000.0)
		tmp = t_1;
	elseif (a <= -3.45e-304)
		tmp = Float64(Float64(Float64(y / z) - 1.0) * Float64(-t));
	elseif (a <= 2.9e-11)
		tmp = Float64(Float64(y / Float64(z - a)) * Float64(x - t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[a, -14600000.0], t$95$1, If[LessEqual[a, -3.45e-304], N[(N[(N[(y / z), $MachinePrecision] - 1.0), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[a, 2.9e-11], N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.46e7 or 2.9e-11 < a

   1. Initial program 71.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 75.4

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

   5. Applied rewrites 75.4%

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

   if -1.46e7 < a < -3.4499999999999999e-304

   1. Initial program 71.6%

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

   3. Taylor expanded in t around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 60.6

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

   5. Applied rewrites 60.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 65.4%

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

   10. Applied rewrites 65.4%

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

   if -3.4499999999999999e-304 < a < 2.9e-11

   1. Initial program 72.2%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 60.2

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

   5. Applied rewrites 60.2%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -14600000:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \mathbf{elif}\;a \leq -3.45 \cdot 10^{-304}:\\ \;\;\;\;\left(\frac{y}{z} - 1\right) \cdot \left(-t\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-11}:\\ \;\;\;\;\frac{y}{z - a} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+127}:\\ \;\;\;\;t - \left(a - y\right) \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+86}:\\ \;\;\;\;x - \frac{\left(z - y\right) \cdot \left(x - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{y - a}{z}, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.05e+127)
   (- t (* (- a y) (/ (- x t) z)))
   (if (<= z 3e+86)
     (- x (/ (* (- z y) (- x t)) (- z a)))
     (fma (- x t) (/ (- y a) z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.05e+127) {
		tmp = t - ((a - y) * ((x - t) / z));
	} else if (z <= 3e+86) {
		tmp = x - (((z - y) * (x - t)) / (z - a));
	} else {
		tmp = fma((x - t), ((y - a) / z), t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.05e+127)
		tmp = Float64(t - Float64(Float64(a - y) * Float64(Float64(x - t) / z)));
	elseif (z <= 3e+86)
		tmp = Float64(x - Float64(Float64(Float64(z - y) * Float64(x - t)) / Float64(z - a)));
	else
		tmp = fma(Float64(x - t), Float64(Float64(y - a) / z), t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.05e+127], N[(t - N[(N[(a - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+86], N[(x - N[(N[(N[(z - y), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - t), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.04999999999999991e127

   1. Initial program 37.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 55.1

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

   4. Applied rewrites 55.1%

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

   5. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. lower--.f64 N/A

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

      7. div-sub N/A

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

      8. associate-/l* N/A

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

      9. associate-/l* N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 88.0

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

   7. Applied rewrites 88.0%

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

   if -2.04999999999999991e127 < z < 2.99999999999999977e86

   1. Initial program 86.2%

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

   if 2.99999999999999977e86 < z

   1. Initial program 34.6%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 76.2

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

   5. Applied rewrites 76.2%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+127}:\\ \;\;\;\;t - \left(a - y\right) \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+86}:\\ \;\;\;\;x - \frac{\left(z - y\right) \cdot \left(x - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{y - a}{z}, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+80}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+66}:\\ \;\;\;\;\mathsf{fma}\left(-t, \frac{y}{z}, t\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+172}:\\ \;\;\;\;\frac{y - z}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.5e+80)
   (* 1.0 x)
   (if (<= a 3.3e+66)
     (fma (- t) (/ y z) t)
     (if (<= a 8.2e+172) (* (/ (- y z) a) t) (* 1.0 x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.5e+80) {
		tmp = 1.0 * x;
	} else if (a <= 3.3e+66) {
		tmp = fma(-t, (y / z), t);
	} else if (a <= 8.2e+172) {
		tmp = ((y - z) / a) * t;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.5e+80)
		tmp = Float64(1.0 * x);
	elseif (a <= 3.3e+66)
		tmp = fma(Float64(-t), Float64(y / z), t);
	elseif (a <= 8.2e+172)
		tmp = Float64(Float64(Float64(y - z) / a) * t);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.5e+80], N[(1.0 * x), $MachinePrecision], If[LessEqual[a, 3.3e+66], N[((-t) * N[(y / z), $MachinePrecision] + t), $MachinePrecision], If[LessEqual[a, 8.2e+172], N[(N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] * t), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.49999999999999994e80 or 8.200000000000001e172 < a

   1. Initial program 70.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 97.5

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

   4. Applied rewrites 97.5%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. times-frac N/A

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

      5. distribute-rgt-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-/.f64 86.1

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

   7. Applied rewrites 86.1%

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

   8. Taylor expanded in a around inf

      \[\leadsto 1 \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 57.6%

       \[\leadsto 1 \cdot x \]

   if -3.49999999999999994e80 < a < 3.3000000000000001e66

   1. Initial program 72.5%

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

   3. Taylor expanded in t around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 50.0

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

   5. Applied rewrites 50.0%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 51.5%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 51.5%

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

   if 3.3000000000000001e66 < a < 8.200000000000001e172

   1. Initial program 72.7%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 85.1

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

   5. Applied rewrites 85.1%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 52.2%

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

Alternative 5: 76.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y - z}{a}, t - x, x\right)\\ \mathbf{if}\;a \leq -75000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{y - a}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- y z) a) (- t x) x)))
   (if (<= a -75000000000.0)
     t_1
     (if (<= a 6e-11) (fma (- x t) (/ (- y a) z) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((y - z) / a), (t - x), x);
	double tmp;
	if (a <= -75000000000.0) {
		tmp = t_1;
	} else if (a <= 6e-11) {
		tmp = fma((x - t), ((y - a) / z), t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(y - z) / a), Float64(t - x), x)
	tmp = 0.0
	if (a <= -75000000000.0)
		tmp = t_1;
	elseif (a <= 6e-11)
		tmp = fma(Float64(x - t), Float64(Float64(y - a) / z), t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -75000000000.0], t$95$1, If[LessEqual[a, 6e-11], N[(N[(x - t), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -7.5e10 or 6e-11 < a

   1. Initial program 71.8%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 83.7

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

   5. Applied rewrites 83.7%

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

   if -7.5e10 < a < 6e-11

   1. Initial program 71.9%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 81.7

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

   5. Applied rewrites 81.7%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -75000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a}, t - x, x\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{y - a}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a}, t - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y - z}{a}, t - x, x\right)\\ \mathbf{if}\;a \leq -3.9 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-74}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{z}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- y z) a) (- t x) x)))
   (if (<= a -3.9e-61)
     t_1
     (if (<= a 2.2e-74) (fma (/ (- z y) z) (- t x) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((y - z) / a), (t - x), x);
	double tmp;
	if (a <= -3.9e-61) {
		tmp = t_1;
	} else if (a <= 2.2e-74) {
		tmp = fma(((z - y) / z), (t - x), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(y - z) / a), Float64(t - x), x)
	tmp = 0.0
	if (a <= -3.9e-61)
		tmp = t_1;
	elseif (a <= 2.2e-74)
		tmp = fma(Float64(Float64(z - y) / z), Float64(t - x), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -3.9e-61], t$95$1, If[LessEqual[a, 2.2e-74], N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.90000000000000033e-61 or 2.2000000000000001e-74 < a

   1. Initial program 70.3%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 76.6

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

   5. Applied rewrites 76.6%

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

   if -3.90000000000000033e-61 < a < 2.2000000000000001e-74

   1. Initial program 74.3%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. mul-1-neg N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 70.2

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

   5. Applied rewrites 70.2%

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

Alternative 7: 62.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{z - a} \cdot \left(z - y\right)\\ \mathbf{if}\;t \leq -3.45 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(z - y, \frac{x}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ t (- z a)) (- z y))))
   (if (<= t -3.45e-43)
     t_1
     (if (<= t 6e+29) (fma (- z y) (/ x (- a z)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t / (z - a)) * (z - y);
	double tmp;
	if (t <= -3.45e-43) {
		tmp = t_1;
	} else if (t <= 6e+29) {
		tmp = fma((z - y), (x / (a - z)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t / Float64(z - a)) * Float64(z - y))
	tmp = 0.0
	if (t <= -3.45e-43)
		tmp = t_1;
	elseif (t <= 6e+29)
		tmp = fma(Float64(z - y), Float64(x / Float64(a - z)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.45e-43], t$95$1, If[LessEqual[t, 6e+29], N[(N[(z - y), $MachinePrecision] * N[(x / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.44999999999999982e-43 or 5.9999999999999998e29 < t

   1. Initial program 67.6%

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

   3. Taylor expanded in t around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 75.7

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

   5. Applied rewrites 75.7%

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

   if -3.44999999999999982e-43 < t < 5.9999999999999998e29

   1. Initial program 76.4%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. unsub-neg N/A

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

      13. remove-double-neg N/A

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

      14. lower--.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 70.8

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

   5. Applied rewrites 70.8%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.45 \cdot 10^{-43}:\\ \;\;\;\;\frac{t}{z - a} \cdot \left(z - y\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(z - y, \frac{x}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z - a} \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{z - a} \cdot \left(z - y\right)\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{-41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ t (- z a)) (- z y))))
   (if (<= t -1.5e-41) t_1 (if (<= t 5.9e+29) (fma (/ (- t x) a) y x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t / (z - a)) * (z - y);
	double tmp;
	if (t <= -1.5e-41) {
		tmp = t_1;
	} else if (t <= 5.9e+29) {
		tmp = fma(((t - x) / a), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t / Float64(z - a)) * Float64(z - y))
	tmp = 0.0
	if (t <= -1.5e-41)
		tmp = t_1;
	elseif (t <= 5.9e+29)
		tmp = fma(Float64(Float64(t - x) / a), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.5e-41], t$95$1, If[LessEqual[t, 5.9e+29], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.49999999999999994e-41 or 5.8999999999999999e29 < t

   1. Initial program 67.6%

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

   3. Taylor expanded in t around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 75.7

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

   5. Applied rewrites 75.7%

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

   if -1.49999999999999994e-41 < t < 5.8999999999999999e29

   1. Initial program 76.4%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 59.2

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

   5. Applied rewrites 59.2%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-41}:\\ \;\;\;\;\frac{t}{z - a} \cdot \left(z - y\right)\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z - a} \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \mathbf{if}\;a \leq -14600000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-74}:\\ \;\;\;\;\left(\frac{y}{z} - 1\right) \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- t x) a) y x)))
   (if (<= a -14600000.0)
     t_1
     (if (<= a 4.7e-74) (* (- (/ y z) 1.0) (- t)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((t - x) / a), y, x);
	double tmp;
	if (a <= -14600000.0) {
		tmp = t_1;
	} else if (a <= 4.7e-74) {
		tmp = ((y / z) - 1.0) * -t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(t - x) / a), y, x)
	tmp = 0.0
	if (a <= -14600000.0)
		tmp = t_1;
	elseif (a <= 4.7e-74)
		tmp = Float64(Float64(Float64(y / z) - 1.0) * Float64(-t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[a, -14600000.0], t$95$1, If[LessEqual[a, 4.7e-74], N[(N[(N[(y / z), $MachinePrecision] - 1.0), $MachinePrecision] * (-t)), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.46e7 or 4.7000000000000001e-74 < a

   1. Initial program 71.1%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 72.3

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

   5. Applied rewrites 72.3%

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

   if -1.46e7 < a < 4.7000000000000001e-74

   1. Initial program 72.8%

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

   3. Taylor expanded in t around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 56.4

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

   5. Applied rewrites 56.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 60.4%

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

   10. Applied rewrites 60.4%

       \[\leadsto \left(-t\right) \cdot \left(\frac{y}{z} - 1\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -14600000:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-74}:\\ \;\;\;\;\left(\frac{y}{z} - 1\right) \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \mathbf{if}\;a \leq -14600000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-74}:\\ \;\;\;\;\mathsf{fma}\left(-t, \frac{y}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- t x) a) y x)))
   (if (<= a -14600000.0) t_1 (if (<= a 4.7e-74) (fma (- t) (/ y z) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((t - x) / a), y, x);
	double tmp;
	if (a <= -14600000.0) {
		tmp = t_1;
	} else if (a <= 4.7e-74) {
		tmp = fma(-t, (y / z), t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(t - x) / a), y, x)
	tmp = 0.0
	if (a <= -14600000.0)
		tmp = t_1;
	elseif (a <= 4.7e-74)
		tmp = fma(Float64(-t), Float64(y / z), t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[a, -14600000.0], t$95$1, If[LessEqual[a, 4.7e-74], N[((-t) * N[(y / z), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.46e7 or 4.7000000000000001e-74 < a

   1. Initial program 71.1%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 72.3

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

   5. Applied rewrites 72.3%

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

   if -1.46e7 < a < 4.7000000000000001e-74

   1. Initial program 72.8%

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

   3. Taylor expanded in t around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 56.4

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

   5. Applied rewrites 56.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 60.4%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 60.4%

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

Alternative 11: 60.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \mathbf{if}\;a \leq -14600000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-74}:\\ \;\;\;\;\mathsf{fma}\left(-t, \frac{y}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ y a) (- t x) x)))
   (if (<= a -14600000.0) t_1 (if (<= a 4.7e-74) (fma (- t) (/ y z) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y / a), (t - x), x);
	double tmp;
	if (a <= -14600000.0) {
		tmp = t_1;
	} else if (a <= 4.7e-74) {
		tmp = fma(-t, (y / z), t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y / a), Float64(t - x), x)
	tmp = 0.0
	if (a <= -14600000.0)
		tmp = t_1;
	elseif (a <= 4.7e-74)
		tmp = fma(Float64(-t), Float64(y / z), t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -14600000.0], t$95$1, If[LessEqual[a, 4.7e-74], N[((-t) * N[(y / z), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.46e7 or 4.7000000000000001e-74 < a

   1. Initial program 71.1%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 79.5

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

   5. Applied rewrites 79.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 72.3%

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

   if -1.46e7 < a < 4.7000000000000001e-74

   1. Initial program 72.8%

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

   3. Taylor expanded in t around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 56.4

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

   5. Applied rewrites 56.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 60.4%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 60.4%

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

Alternative 12: 51.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{a}, -x, x\right)\\ \mathbf{if}\;a \leq -19000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-74}:\\ \;\;\;\;\mathsf{fma}\left(-t, \frac{y}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ y a) (- x) x)))
   (if (<= a -19000000.0) t_1 (if (<= a 4.8e-74) (fma (- t) (/ y z) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y / a), -x, x);
	double tmp;
	if (a <= -19000000.0) {
		tmp = t_1;
	} else if (a <= 4.8e-74) {
		tmp = fma(-t, (y / z), t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y / a), Float64(-x), x)
	tmp = 0.0
	if (a <= -19000000.0)
		tmp = t_1;
	elseif (a <= 4.8e-74)
		tmp = fma(Float64(-t), Float64(y / z), t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * (-x) + x), $MachinePrecision]}, If[LessEqual[a, -19000000.0], t$95$1, If[LessEqual[a, 4.8e-74], N[((-t) * N[(y / z), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.9e7 or 4.7999999999999998e-74 < a

   1. Initial program 71.1%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 79.5

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

   5. Applied rewrites 79.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 72.3%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 53.4%

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

   if -1.9e7 < a < 4.7999999999999998e-74

   1. Initial program 72.8%

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

   3. Taylor expanded in t around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 56.4

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

   5. Applied rewrites 56.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 60.4%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 60.4%

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

Alternative 13: 47.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+80}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-33}:\\ \;\;\;\;\mathsf{fma}\left(-t, \frac{y}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.5e+80)
   (* 1.0 x)
   (if (<= a 4.6e-33) (fma (- t) (/ y z) t) (* 1.0 x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.5e+80) {
		tmp = 1.0 * x;
	} else if (a <= 4.6e-33) {
		tmp = fma(-t, (y / z), t);
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.5e+80)
		tmp = Float64(1.0 * x);
	elseif (a <= 4.6e-33)
		tmp = fma(Float64(-t), Float64(y / z), t);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.5e+80], N[(1.0 * x), $MachinePrecision], If[LessEqual[a, 4.6e-33], N[((-t) * N[(y / z), $MachinePrecision] + t), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.49999999999999994e80 or 4.59999999999999971e-33 < a

   1. Initial program 69.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 92.2

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

   4. Applied rewrites 92.2%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. times-frac N/A

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

      5. distribute-rgt-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-/.f64 82.0

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

   7. Applied rewrites 82.0%

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

   8. Taylor expanded in a around inf

      \[\leadsto 1 \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 47.7%

       \[\leadsto 1 \cdot x \]

   if -3.49999999999999994e80 < a < 4.59999999999999971e-33

   1. Initial program 73.7%

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

   3. Taylor expanded in t around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 53.7

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

   5. Applied rewrites 53.7%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 55.5%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 55.5%

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

Alternative 14: 34.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -1 \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-224}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+32}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -1.0 (- t))))
   (if (<= z -2.9e+173)
     t_1
     (if (<= z 1.35e-224) (* (/ y a) t) (if (<= z 1.65e+32) (* 1.0 x) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -1.0 * -t;
	double tmp;
	if (z <= -2.9e+173) {
		tmp = t_1;
	} else if (z <= 1.35e-224) {
		tmp = (y / a) * t;
	} else if (z <= 1.65e+32) {
		tmp = 1.0 * 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 = (-1.0d0) * -t
    if (z <= (-2.9d+173)) then
        tmp = t_1
    else if (z <= 1.35d-224) then
        tmp = (y / a) * t
    else if (z <= 1.65d+32) then
        tmp = 1.0d0 * 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 = -1.0 * -t;
	double tmp;
	if (z <= -2.9e+173) {
		tmp = t_1;
	} else if (z <= 1.35e-224) {
		tmp = (y / a) * t;
	} else if (z <= 1.65e+32) {
		tmp = 1.0 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -1.0 * -t
	tmp = 0
	if z <= -2.9e+173:
		tmp = t_1
	elif z <= 1.35e-224:
		tmp = (y / a) * t
	elif z <= 1.65e+32:
		tmp = 1.0 * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-1.0 * Float64(-t))
	tmp = 0.0
	if (z <= -2.9e+173)
		tmp = t_1;
	elseif (z <= 1.35e-224)
		tmp = Float64(Float64(y / a) * t);
	elseif (z <= 1.65e+32)
		tmp = Float64(1.0 * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -1.0 * -t;
	tmp = 0.0;
	if (z <= -2.9e+173)
		tmp = t_1;
	elseif (z <= 1.35e-224)
		tmp = (y / a) * t;
	elseif (z <= 1.65e+32)
		tmp = 1.0 * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-1.0 * (-t)), $MachinePrecision]}, If[LessEqual[z, -2.9e+173], t$95$1, If[LessEqual[z, 1.35e-224], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 1.65e+32], N[(1.0 * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.90000000000000007e173 or 1.6500000000000001e32 < z

   1. Initial program 42.2%

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

   3. Taylor expanded in t around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 56.5

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

   5. Applied rewrites 56.5%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 57.6%

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

   9. Taylor expanded in z around inf

      \[\leadsto \left(\mathsf{neg}\left(t\right)\right) \cdot -1 \]
   10. Step-by-step derivation

   11. Applied rewrites 50.4%

       \[\leadsto \left(-t\right) \cdot -1 \]

   if -2.90000000000000007e173 < z < 1.34999999999999999e-224

   1. Initial program 80.0%

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

   3. Taylor expanded in t around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 46.0

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

   5. Applied rewrites 46.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 37.3%

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

   if 1.34999999999999999e-224 < z < 1.6500000000000001e32

   1. Initial program 92.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 92.1

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

   4. Applied rewrites 92.1%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. times-frac N/A

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

      5. distribute-rgt-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-/.f64 79.7

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

   7. Applied rewrites 79.7%

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

   8. Taylor expanded in a around inf

      \[\leadsto 1 \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 41.5%

       \[\leadsto 1 \cdot x \]
3. Recombined 3 regimes into one program.

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+173}:\\ \;\;\;\;-1 \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-224}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+32}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 37.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.0074:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-33}:\\ \;\;\;\;-1 \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -0.0074) (* 1.0 x) (if (<= a 4e-33) (* -1.0 (- t)) (* 1.0 x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.0074) {
		tmp = 1.0 * x;
	} else if (a <= 4e-33) {
		tmp = -1.0 * -t;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-0.0074d0)) then
        tmp = 1.0d0 * x
    else if (a <= 4d-33) then
        tmp = (-1.0d0) * -t
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.0074) {
		tmp = 1.0 * x;
	} else if (a <= 4e-33) {
		tmp = -1.0 * -t;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -0.0074:
		tmp = 1.0 * x
	elif a <= 4e-33:
		tmp = -1.0 * -t
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -0.0074)
		tmp = Float64(1.0 * x);
	elseif (a <= 4e-33)
		tmp = Float64(-1.0 * Float64(-t));
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -0.0074)
		tmp = 1.0 * x;
	elseif (a <= 4e-33)
		tmp = -1.0 * -t;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -0.0074], N[(1.0 * x), $MachinePrecision], If[LessEqual[a, 4e-33], N[(-1.0 * (-t)), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -0.0074000000000000003 or 4.0000000000000002e-33 < a

   1. Initial program 70.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 91.2

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

   4. Applied rewrites 91.2%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. times-frac N/A

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

      5. distribute-rgt-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-/.f64 80.3

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

   7. Applied rewrites 80.3%

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

   8. Taylor expanded in a around inf

      \[\leadsto 1 \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 43.7%

       \[\leadsto 1 \cdot x \]

   if -0.0074000000000000003 < a < 4.0000000000000002e-33

   1. Initial program 73.5%

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

   3. Taylor expanded in t around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 55.3

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

   5. Applied rewrites 55.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 59.1%

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

   9. Taylor expanded in z around inf

      \[\leadsto \left(\mathsf{neg}\left(t\right)\right) \cdot -1 \]
   10. Step-by-step derivation

   11. Applied rewrites 37.0%

       \[\leadsto \left(-t\right) \cdot -1 \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0074:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-33}:\\ \;\;\;\;-1 \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 33.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.0074:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-33}:\\ \;\;\;\;\left(t - x\right) + x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -0.0074) (* 1.0 x) (if (<= a 4e-33) (+ (- t x) x) (* 1.0 x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.0074) {
		tmp = 1.0 * x;
	} else if (a <= 4e-33) {
		tmp = (t - x) + x;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-0.0074d0)) then
        tmp = 1.0d0 * x
    else if (a <= 4d-33) then
        tmp = (t - x) + x
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.0074) {
		tmp = 1.0 * x;
	} else if (a <= 4e-33) {
		tmp = (t - x) + x;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -0.0074:
		tmp = 1.0 * x
	elif a <= 4e-33:
		tmp = (t - x) + x
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -0.0074)
		tmp = Float64(1.0 * x);
	elseif (a <= 4e-33)
		tmp = Float64(Float64(t - x) + x);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -0.0074)
		tmp = 1.0 * x;
	elseif (a <= 4e-33)
		tmp = (t - x) + x;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -0.0074], N[(1.0 * x), $MachinePrecision], If[LessEqual[a, 4e-33], N[(N[(t - x), $MachinePrecision] + x), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -0.0074000000000000003 or 4.0000000000000002e-33 < a

   1. Initial program 70.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 91.2

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

   4. Applied rewrites 91.2%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. times-frac N/A

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

      5. distribute-rgt-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-/.f64 80.3

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

   7. Applied rewrites 80.3%

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

   8. Taylor expanded in a around inf

      \[\leadsto 1 \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 43.7%

       \[\leadsto 1 \cdot x \]

   if -0.0074000000000000003 < a < 4.0000000000000002e-33

   1. Initial program 73.5%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 29.6

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

   5. Applied rewrites 29.6%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0074:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-33}:\\ \;\;\;\;\left(t - x\right) + x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 25.1% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ 1 \cdot x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* 1.0 x))

C

double code(double x, double y, double z, double t, double a) {
	return 1.0 * 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 = 1.0d0 * x
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 1.0 * x;
}

Python

def code(x, y, z, t, a):
	return 1.0 * x

Julia

function code(x, y, z, t, a)
	return Float64(1.0 * x)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 1.0 * x;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(1.0 * x), $MachinePrecision]

Derivation

1. Initial program 71.8%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l* N/A

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

   4. clear-num N/A

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

   5. un-div-inv N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 83.9

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

4. Applied rewrites 83.9%

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

5. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. +-commutative N/A

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

   4. times-frac N/A

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

   5. distribute-rgt-out N/A

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

   6. lower-fma.f64 N/A

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

   7. lower-/.f64 N/A

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

   8. lower--.f64 N/A

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

   9. lower--.f64 N/A

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

   10. lower-+.f64 N/A

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

   11. lower-/.f64 76.6

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

7. Applied rewrites 76.6%

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

8. Taylor expanded in a around inf

   \[\leadsto 1 \cdot x \]
9. Step-by-step derivation

10. Applied rewrites 27.2%

    \[\leadsto 1 \cdot x \]
11. Add Preprocessing

Developer Target 1: 83.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024235 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

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

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