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

Percentage Accurate: 67.8% → 90.0%

Time: 15.3s

Alternatives: 17

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-235} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -2e-235) (not (<= t_1 0.0)))
     (fma (- y x) (/ (- z t) (- a t)) x)
     (- y (/ (* x (- a z)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -2e-235) || !(t_1 <= 0.0)) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else {
		tmp = y - ((x * (a - z)) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -2e-235) || !(t_1 <= 0.0))
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	else
		tmp = Float64(y - Float64(Float64(x * Float64(a - z)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-235], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y - N[(N[(x * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.9999999999999999e-235 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 71.4%

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

      1. +-commutative 71.4%

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

      2. associate-/l* 88.5%

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

      3. fma-define 88.6%

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

   3. Simplified 88.6%

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

   if -1.9999999999999999e-235 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.2%

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

      1. +-commutative 4.2%

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

      2. associate-/l* 4.2%

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

      3. fma-define 4.2%

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

   3. Simplified 4.2%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. div-sub 99.8%

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

      6. mul-1-neg 99.8%

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

      7. distribute-lft-out-- 99.8%

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

      8. associate-*r/ 99.8%

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

      9. mul-1-neg 99.8%

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

      10. unsub-neg 99.8%

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

      11. distribute-rgt-out-- 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around 0 99.8%

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

      1. mul-1-neg 99.8%

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

      2. distribute-rgt-neg-in 99.8%

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

      3. sub-neg 99.8%

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

      4. distribute-neg-in 99.8%

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

      5. remove-double-neg 99.8%

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

      6. +-commutative 99.8%

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

      7. sub-neg 99.8%

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

   10. Simplified 99.8%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-235} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \frac{x - y}{t}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-235}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y - \frac{x \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+295}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* z (/ (- x y) t))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-235)
       t_2
       (if (<= t_2 0.0)
         (- y (/ (* x (- a z)) t))
         (if (<= t_2 2e+295) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (z * ((x - y) / t));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-235) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - ((x * (a - z)) / t);
	} else if (t_2 <= 2e+295) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (z * ((x - y) / t));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-235) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - ((x * (a - z)) / t);
	} else if (t_2 <= 2e+295) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (z * ((x - y) / t))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-235:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y - ((x * (a - z)) / t)
	elif t_2 <= 2e+295:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(z * Float64(Float64(x - y) / t)))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-235)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y - Float64(Float64(x * Float64(a - z)) / t));
	elseif (t_2 <= 2e+295)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (z * ((x - y) / t));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-235)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y - ((x * (a - z)) / t);
	elseif (t_2 <= 2e+295)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-235], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y - N[(N[(x * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+295], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or 2e295 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 36.3%

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

      1. +-commutative 36.3%

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

      2. associate-/l* 79.4%

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

      3. fma-define 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in t around inf 58.0%

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

      1. associate--l+ 58.0%

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

      2. associate-*r/ 58.0%

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

      3. associate-*r/ 58.0%

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

      4. mul-1-neg 58.0%

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

      5. div-sub 59.0%

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

      6. mul-1-neg 59.0%

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

      7. distribute-lft-out-- 59.0%

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

      8. associate-*r/ 59.0%

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

      9. mul-1-neg 59.0%

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

      10. unsub-neg 59.0%

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

      11. distribute-rgt-out-- 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in z around inf 60.3%

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

      1. associate-/l* 68.7%

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

   10. Simplified 68.7%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.9999999999999999e-235 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 2e295

   1. Initial program 96.4%

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

   if -1.9999999999999999e-235 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.2%

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

      1. +-commutative 4.2%

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

      2. associate-/l* 4.2%

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

      3. fma-define 4.2%

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

   3. Simplified 4.2%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. div-sub 99.8%

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

      6. mul-1-neg 99.8%

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

      7. distribute-lft-out-- 99.8%

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

      8. associate-*r/ 99.8%

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

      9. mul-1-neg 99.8%

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

      10. unsub-neg 99.8%

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

      11. distribute-rgt-out-- 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around 0 99.8%

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

      1. mul-1-neg 99.8%

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

      2. distribute-rgt-neg-in 99.8%

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

      3. sub-neg 99.8%

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

      4. distribute-neg-in 99.8%

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

      5. remove-double-neg 99.8%

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

      6. +-commutative 99.8%

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

      7. sub-neg 99.8%

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

   10. Simplified 99.8%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-235}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y - \frac{x \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 2 \cdot 10^{+295}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{1}{a - t}\right)\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-235}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y - \frac{x \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (* (- y x) (/ 1.0 (- a t))))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-235)
       t_2
       (if (<= t_2 0.0) (- y (/ (* x (- a z)) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) * (1.0 / (a - t))));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-235) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - ((x * (a - z)) / t);
	} 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 - t) * ((y - x) * (1.0 / (a - t))));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-235) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - ((x * (a - z)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * ((y - x) * (1.0 / (a - t))))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-235:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y - ((x * (a - z)) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) * Float64(1.0 / Float64(a - t)))))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-235)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y - Float64(Float64(x * Float64(a - z)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * ((y - x) * (1.0 / (a - t))));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-235)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y - ((x * (a - z)) / t);
	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 - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-235], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y - N[(N[(x * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 58.8%

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

      1. div-inv 58.7%

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

      2. *-commutative 58.7%

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

      3. associate-*l* 84.1%

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

   4. Applied egg-rr 84.1%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.9999999999999999e-235

   1. Initial program 95.4%

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

   if -1.9999999999999999e-235 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.2%

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

      1. +-commutative 4.2%

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

      2. associate-/l* 4.2%

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

      3. fma-define 4.2%

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

   3. Simplified 4.2%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. div-sub 99.8%

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

      6. mul-1-neg 99.8%

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

      7. distribute-lft-out-- 99.8%

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

      8. associate-*r/ 99.8%

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

      9. mul-1-neg 99.8%

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

      10. unsub-neg 99.8%

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

      11. distribute-rgt-out-- 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around 0 99.8%

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

      1. mul-1-neg 99.8%

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

      2. distribute-rgt-neg-in 99.8%

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

      3. sub-neg 99.8%

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

      4. distribute-neg-in 99.8%

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

      5. remove-double-neg 99.8%

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

      6. +-commutative 99.8%

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

      7. sub-neg 99.8%

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

   10. Simplified 99.8%

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

Alternative 4: 65.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-48}:\\ \;\;\;\;y - \frac{x \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;a \leq 1.56 \cdot 10^{-40}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.3e+78)
   (* x (+ (/ (- z t) (- t a)) 1.0))
   (if (<= a -1.5e-48)
     (- y (/ (* x (- a z)) t))
     (if (<= a 1.56e-40)
       (+ y (* z (/ (- x y) t)))
       (- x (* z (/ (- x y) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.3e+78) {
		tmp = x * (((z - t) / (t - a)) + 1.0);
	} else if (a <= -1.5e-48) {
		tmp = y - ((x * (a - z)) / t);
	} else if (a <= 1.56e-40) {
		tmp = y + (z * ((x - y) / t));
	} else {
		tmp = x - (z * ((x - y) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.3d+78)) then
        tmp = x * (((z - t) / (t - a)) + 1.0d0)
    else if (a <= (-1.5d-48)) then
        tmp = y - ((x * (a - z)) / t)
    else if (a <= 1.56d-40) then
        tmp = y + (z * ((x - y) / t))
    else
        tmp = x - (z * ((x - y) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.3e+78) {
		tmp = x * (((z - t) / (t - a)) + 1.0);
	} else if (a <= -1.5e-48) {
		tmp = y - ((x * (a - z)) / t);
	} else if (a <= 1.56e-40) {
		tmp = y + (z * ((x - y) / t));
	} else {
		tmp = x - (z * ((x - y) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.3e+78:
		tmp = x * (((z - t) / (t - a)) + 1.0)
	elif a <= -1.5e-48:
		tmp = y - ((x * (a - z)) / t)
	elif a <= 1.56e-40:
		tmp = y + (z * ((x - y) / t))
	else:
		tmp = x - (z * ((x - y) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.3e+78)
		tmp = Float64(x * Float64(Float64(Float64(z - t) / Float64(t - a)) + 1.0));
	elseif (a <= -1.5e-48)
		tmp = Float64(y - Float64(Float64(x * Float64(a - z)) / t));
	elseif (a <= 1.56e-40)
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	else
		tmp = Float64(x - Float64(z * Float64(Float64(x - y) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.3e+78)
		tmp = x * (((z - t) / (t - a)) + 1.0);
	elseif (a <= -1.5e-48)
		tmp = y - ((x * (a - z)) / t);
	elseif (a <= 1.56e-40)
		tmp = y + (z * ((x - y) / t));
	else
		tmp = x - (z * ((x - y) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.3e+78], N[(x * N[(N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.5e-48], N[(y - N[(N[(x * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.56e-40], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(N[(x - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.3000000000000002e78

   1. Initial program 66.4%

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

      1. +-commutative 66.4%

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

      2. associate-/l* 95.0%

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

      3. fma-define 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in y around 0 57.1%

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

      1. *-rgt-identity 57.1%

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

      2. mul-1-neg 57.1%

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

      3. associate-/l* 73.4%

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

      4. distribute-rgt-neg-in 73.4%

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

      5. mul-1-neg 73.4%

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

      6. distribute-lft-in 73.5%

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

      7. mul-1-neg 73.5%

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

      8. unsub-neg 73.5%

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

   7. Simplified 73.5%

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

   if -2.3000000000000002e78 < a < -1.5e-48

   1. Initial program 61.5%

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

      1. +-commutative 61.5%

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

      2. associate-/l* 65.5%

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

      3. fma-define 65.6%

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

   3. Simplified 65.6%

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

   5. Taylor expanded in t around inf 59.1%

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

      1. associate--l+ 59.1%

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

      2. associate-*r/ 59.1%

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

      3. associate-*r/ 59.1%

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

      4. mul-1-neg 59.1%

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

      5. div-sub 59.2%

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

      6. mul-1-neg 59.2%

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

      7. distribute-lft-out-- 59.2%

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

      8. associate-*r/ 59.2%

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

      9. mul-1-neg 59.2%

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

      10. unsub-neg 59.2%

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

      11. distribute-rgt-out-- 59.2%

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

   7. Simplified 59.2%

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

   8. Taylor expanded in y around 0 59.8%

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

      1. mul-1-neg 59.8%

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

      2. distribute-rgt-neg-in 59.8%

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

      3. sub-neg 59.8%

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

      4. distribute-neg-in 59.8%

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

      5. remove-double-neg 59.8%

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

      6. +-commutative 59.8%

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

      7. sub-neg 59.8%

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

   10. Simplified 59.8%

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

   if -1.5e-48 < a < 1.55999999999999996e-40

   1. Initial program 63.9%

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

      1. +-commutative 63.9%

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

      2. associate-/l* 76.0%

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

      3. fma-define 76.0%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in t around inf 79.7%

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

      1. associate--l+ 79.7%

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

      2. associate-*r/ 79.7%

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

      3. associate-*r/ 79.7%

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

      4. mul-1-neg 79.7%

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

      5. div-sub 80.8%

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

      6. mul-1-neg 80.8%

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

      7. distribute-lft-out-- 80.8%

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

      8. associate-*r/ 80.8%

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

      9. mul-1-neg 80.8%

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

      10. unsub-neg 80.8%

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

      11. distribute-rgt-out-- 80.8%

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

   7. Simplified 80.8%

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

   8. Taylor expanded in z around inf 78.0%

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

      1. associate-/l* 80.5%

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

   10. Simplified 80.5%

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

   if 1.55999999999999996e-40 < a

   1. Initial program 71.8%

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

   3. Taylor expanded in t around 0 64.4%

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

      1. associate-/l* 70.3%

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

   5. Simplified 70.3%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-48}:\\ \;\;\;\;y - \frac{x \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;a \leq 1.56 \cdot 10^{-40}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + y \cdot \frac{a - z}{t}\\ \mathbf{if}\;t \leq -530000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-232}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-12}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* y (/ (- a z) t)))))
   (if (<= t -530000000000.0)
     t_1
     (if (<= t -9e-232)
       (+ x (* y (/ (- z t) a)))
       (if (<= t 6.5e-12) (- x (* z (/ (- x y) a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (y * ((a - z) / t));
	double tmp;
	if (t <= -530000000000.0) {
		tmp = t_1;
	} else if (t <= -9e-232) {
		tmp = x + (y * ((z - t) / a));
	} else if (t <= 6.5e-12) {
		tmp = x - (z * ((x - y) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (y * ((a - z) / t))
    if (t <= (-530000000000.0d0)) then
        tmp = t_1
    else if (t <= (-9d-232)) then
        tmp = x + (y * ((z - t) / a))
    else if (t <= 6.5d-12) then
        tmp = x - (z * ((x - y) / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (y * ((a - z) / t));
	double tmp;
	if (t <= -530000000000.0) {
		tmp = t_1;
	} else if (t <= -9e-232) {
		tmp = x + (y * ((z - t) / a));
	} else if (t <= 6.5e-12) {
		tmp = x - (z * ((x - y) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (y * ((a - z) / t))
	tmp = 0
	if t <= -530000000000.0:
		tmp = t_1
	elif t <= -9e-232:
		tmp = x + (y * ((z - t) / a))
	elif t <= 6.5e-12:
		tmp = x - (z * ((x - y) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(y * Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (t <= -530000000000.0)
		tmp = t_1;
	elseif (t <= -9e-232)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	elseif (t <= 6.5e-12)
		tmp = Float64(x - Float64(z * Float64(Float64(x - y) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (y * ((a - z) / t));
	tmp = 0.0;
	if (t <= -530000000000.0)
		tmp = t_1;
	elseif (t <= -9e-232)
		tmp = x + (y * ((z - t) / a));
	elseif (t <= 6.5e-12)
		tmp = x - (z * ((x - y) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -530000000000.0], t$95$1, If[LessEqual[t, -9e-232], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e-12], N[(x - N[(z * N[(N[(x - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.3e11 or 6.5000000000000002e-12 < t

   1. Initial program 43.0%

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

      1. +-commutative 43.0%

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

      2. associate-/l* 70.0%

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

      3. fma-define 70.0%

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

   3. Simplified 70.0%

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

   5. Taylor expanded in t around inf 63.9%

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

      1. associate--l+ 63.9%

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

      2. associate-*r/ 63.9%

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

      3. associate-*r/ 63.9%

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

      4. mul-1-neg 63.9%

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

      5. div-sub 63.9%

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

      6. mul-1-neg 63.9%

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

      7. distribute-lft-out-- 63.9%

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

      8. associate-*r/ 63.9%

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

      9. mul-1-neg 63.9%

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

      10. unsub-neg 63.9%

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

      11. distribute-rgt-out-- 64.1%

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

   7. Simplified 64.1%

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

   8. Taylor expanded in y around inf 48.3%

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

      1. associate-/l* 55.9%

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

   10. Simplified 55.9%

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

   if -5.3e11 < t < -8.99999999999999933e-232

   1. Initial program 95.1%

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

   3. Taylor expanded in y around inf 76.2%

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

      1. *-commutative 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in a around inf 78.3%

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

      1. associate-/l* 78.3%

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

   8. Simplified 78.3%

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

   if -8.99999999999999933e-232 < t < 6.5000000000000002e-12

   1. Initial program 91.5%

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

   3. Taylor expanded in t around 0 78.0%

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

      1. associate-/l* 81.7%

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

   5. Simplified 81.7%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -530000000000:\\ \;\;\;\;y + y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-232}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-12}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + y \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+101}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-227}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+24}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.2e+101)
   y
   (if (<= t -9.6e-227)
     (+ x (* y (/ z (- a t))))
     (if (<= t 1.85e+24) (- x (* z (/ (- x y) a))) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.2e+101) {
		tmp = y;
	} else if (t <= -9.6e-227) {
		tmp = x + (y * (z / (a - t)));
	} else if (t <= 1.85e+24) {
		tmp = x - (z * ((x - y) / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.2d+101)) then
        tmp = y
    else if (t <= (-9.6d-227)) then
        tmp = x + (y * (z / (a - t)))
    else if (t <= 1.85d+24) then
        tmp = x - (z * ((x - y) / a))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.2e+101) {
		tmp = y;
	} else if (t <= -9.6e-227) {
		tmp = x + (y * (z / (a - t)));
	} else if (t <= 1.85e+24) {
		tmp = x - (z * ((x - y) / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.2e+101:
		tmp = y
	elif t <= -9.6e-227:
		tmp = x + (y * (z / (a - t)))
	elif t <= 1.85e+24:
		tmp = x - (z * ((x - y) / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.2e+101)
		tmp = y;
	elseif (t <= -9.6e-227)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	elseif (t <= 1.85e+24)
		tmp = Float64(x - Float64(z * Float64(Float64(x - y) / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.2e+101)
		tmp = y;
	elseif (t <= -9.6e-227)
		tmp = x + (y * (z / (a - t)));
	elseif (t <= 1.85e+24)
		tmp = x - (z * ((x - y) / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.2e+101], y, If[LessEqual[t, -9.6e-227], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e+24], N[(x - N[(z * N[(N[(x - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.19999999999999994e101 or 1.85e24 < t

   1. Initial program 37.7%

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

      1. +-commutative 37.7%

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

      2. associate-/l* 66.7%

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

      3. fma-define 66.8%

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

   3. Simplified 66.8%

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

   5. Taylor expanded in y around 0 53.4%

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

      1. +-commutative 53.4%

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

      2. +-commutative 53.4%

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

      3. div-sub 53.4%

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

      4. mul-1-neg 53.4%

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

      5. associate-/l* 66.7%

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

      6. distribute-lft-neg-in 66.7%

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

      7. distribute-rgt-in 66.7%

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

      8. sub-neg 66.7%

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

      9. associate-*l/ 37.7%

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

      10. associate-*r/ 63.5%

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

      11. fma-define 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in t around inf 49.3%

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

   if -1.19999999999999994e101 < t < -9.5999999999999998e-227

   1. Initial program 87.7%

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

   3. Taylor expanded in y around inf 73.7%

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

      1. *-commutative 73.7%

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

   5. Simplified 73.7%

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

   6. Taylor expanded in z around inf 64.8%

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

      1. associate-/l* 69.3%

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

   8. Simplified 69.3%

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

   if -9.5999999999999998e-227 < t < 1.85e24

   1. Initial program 90.1%

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

   3. Taylor expanded in t around 0 73.2%

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

      1. associate-/l* 77.6%

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

   5. Simplified 77.6%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+101}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-227}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+24}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -23000000000000:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-293}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.02 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -23000000000000.0)
   y
   (if (<= t -5.2e-293)
     (+ x (* y (/ z a)))
     (if (<= t 2.02e+24) (* x (- 1.0 (/ z a))) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -23000000000000.0) {
		tmp = y;
	} else if (t <= -5.2e-293) {
		tmp = x + (y * (z / a));
	} else if (t <= 2.02e+24) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-23000000000000.0d0)) then
        tmp = y
    else if (t <= (-5.2d-293)) then
        tmp = x + (y * (z / a))
    else if (t <= 2.02d+24) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -23000000000000.0) {
		tmp = y;
	} else if (t <= -5.2e-293) {
		tmp = x + (y * (z / a));
	} else if (t <= 2.02e+24) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -23000000000000.0:
		tmp = y
	elif t <= -5.2e-293:
		tmp = x + (y * (z / a))
	elif t <= 2.02e+24:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -23000000000000.0)
		tmp = y;
	elseif (t <= -5.2e-293)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 2.02e+24)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -23000000000000.0)
		tmp = y;
	elseif (t <= -5.2e-293)
		tmp = x + (y * (z / a));
	elseif (t <= 2.02e+24)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -23000000000000.0], y, If[LessEqual[t, -5.2e-293], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.02e+24], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.3e13 or 2.0199999999999999e24 < t

   1. Initial program 41.3%

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

      1. +-commutative 41.3%

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

      2. associate-/l* 69.1%

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

      3. fma-define 69.2%

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

   3. Simplified 69.2%

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

   5. Taylor expanded in y around 0 56.6%

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

      1. +-commutative 56.6%

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

      2. +-commutative 56.6%

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

      3. div-sub 56.6%

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

      4. mul-1-neg 56.6%

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

      5. associate-/l* 69.1%

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

      6. distribute-lft-neg-in 69.1%

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

      7. distribute-rgt-in 69.1%

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

      8. sub-neg 69.1%

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

      9. associate-*l/ 41.3%

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

      10. associate-*r/ 66.3%

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

      11. fma-define 66.3%

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

   7. Simplified 66.3%

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

   8. Taylor expanded in t around inf 47.7%

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

   if -2.3e13 < t < -5.1999999999999996e-293

   1. Initial program 93.0%

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

   3. Taylor expanded in y around inf 72.3%

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

      1. *-commutative 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in t around 0 68.7%

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

      1. associate-/l* 70.5%

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

   8. Simplified 70.5%

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

   if -5.1999999999999996e-293 < t < 2.0199999999999999e24

   1. Initial program 90.6%

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

      1. +-commutative 90.6%

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

      2. associate-/l* 96.8%

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

      3. fma-define 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in y around 0 65.1%

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

      1. *-rgt-identity 65.1%

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

      2. mul-1-neg 65.1%

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

      3. associate-/l* 72.7%

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

      4. distribute-rgt-neg-in 72.7%

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

      5. mul-1-neg 72.7%

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

      6. distribute-lft-in 72.7%

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

      7. mul-1-neg 72.7%

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

      8. unsub-neg 72.7%

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

   7. Simplified 72.7%

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

   8. Taylor expanded in t around 0 65.5%

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

Alternative 8: 37.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.75 \cdot 10^{+113}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-279}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+57}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.75e+113)
   x
   (if (<= a -7.5e-279)
     y
     (if (<= a 1.25e-178) (* x (/ z t)) (if (<= a 1.45e+57) y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.75e+113) {
		tmp = x;
	} else if (a <= -7.5e-279) {
		tmp = y;
	} else if (a <= 1.25e-178) {
		tmp = x * (z / t);
	} else if (a <= 1.45e+57) {
		tmp = y;
	} else {
		tmp = 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 <= (-2.75d+113)) then
        tmp = x
    else if (a <= (-7.5d-279)) then
        tmp = y
    else if (a <= 1.25d-178) then
        tmp = x * (z / t)
    else if (a <= 1.45d+57) then
        tmp = y
    else
        tmp = 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 <= -2.75e+113) {
		tmp = x;
	} else if (a <= -7.5e-279) {
		tmp = y;
	} else if (a <= 1.25e-178) {
		tmp = x * (z / t);
	} else if (a <= 1.45e+57) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.75e+113:
		tmp = x
	elif a <= -7.5e-279:
		tmp = y
	elif a <= 1.25e-178:
		tmp = x * (z / t)
	elif a <= 1.45e+57:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.75e+113)
		tmp = x;
	elseif (a <= -7.5e-279)
		tmp = y;
	elseif (a <= 1.25e-178)
		tmp = Float64(x * Float64(z / t));
	elseif (a <= 1.45e+57)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.75e+113)
		tmp = x;
	elseif (a <= -7.5e-279)
		tmp = y;
	elseif (a <= 1.25e-178)
		tmp = x * (z / t);
	elseif (a <= 1.45e+57)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.75e+113], x, If[LessEqual[a, -7.5e-279], y, If[LessEqual[a, 1.25e-178], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e+57], y, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.75e113 or 1.4500000000000001e57 < a

   1. Initial program 69.7%

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

      1. +-commutative 69.7%

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

      2. associate-/l* 93.4%

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

      3. fma-define 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in a around inf 57.2%

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

   if -2.75e113 < a < -7.5e-279 or 1.24999999999999994e-178 < a < 1.4500000000000001e57

   1. Initial program 63.8%

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

      1. +-commutative 63.8%

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

      2. associate-/l* 75.4%

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

      3. fma-define 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in y around 0 71.6%

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

      1. +-commutative 71.6%

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

      2. +-commutative 71.6%

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

      3. div-sub 71.6%

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

      4. mul-1-neg 71.6%

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

      5. associate-/l* 73.8%

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

      6. distribute-lft-neg-in 73.8%

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

      7. distribute-rgt-in 75.4%

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

      8. sub-neg 75.4%

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

      9. associate-*l/ 63.8%

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

      10. associate-*r/ 72.7%

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

      11. fma-define 72.7%

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

   7. Simplified 72.7%

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

   8. Taylor expanded in t around inf 37.5%

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

   if -7.5e-279 < a < 1.24999999999999994e-178

   1. Initial program 69.5%

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

      1. +-commutative 69.5%

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

      2. associate-/l* 79.7%

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

      3. fma-define 79.7%

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

   3. Simplified 79.7%

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

   5. Taylor expanded in y around 0 42.6%

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

      1. *-rgt-identity 42.6%

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

      2. mul-1-neg 42.6%

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

      3. associate-/l* 51.5%

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

      4. distribute-rgt-neg-in 51.5%

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

      5. mul-1-neg 51.5%

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

      6. distribute-lft-in 51.5%

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

      7. mul-1-neg 51.5%

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

      8. unsub-neg 51.5%

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

   7. Simplified 51.5%

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

   8. Taylor expanded in a around 0 55.2%

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

Alternative 9: 73.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+45} \lor \neg \left(a \leq 1.7 \cdot 10^{-40}\right):\\ \;\;\;\;x - \frac{z - t}{a} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4e+45) (not (<= a 1.7e-40)))
   (- x (* (/ (- z t) a) (- x y)))
   (+ y (* z (/ (- x y) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4e+45) || !(a <= 1.7e-40)) {
		tmp = x - (((z - t) / a) * (x - y));
	} else {
		tmp = y + (z * ((x - y) / t));
	}
	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 <= (-4d+45)) .or. (.not. (a <= 1.7d-40))) then
        tmp = x - (((z - t) / a) * (x - y))
    else
        tmp = y + (z * ((x - y) / t))
    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 <= -4e+45) || !(a <= 1.7e-40)) {
		tmp = x - (((z - t) / a) * (x - y));
	} else {
		tmp = y + (z * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4e+45) or not (a <= 1.7e-40):
		tmp = x - (((z - t) / a) * (x - y))
	else:
		tmp = y + (z * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4e+45) || !(a <= 1.7e-40))
		tmp = Float64(x - Float64(Float64(Float64(z - t) / a) * Float64(x - y)));
	else
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4e+45) || ~((a <= 1.7e-40)))
		tmp = x - (((z - t) / a) * (x - y));
	else
		tmp = y + (z * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4e+45], N[Not[LessEqual[a, 1.7e-40]], $MachinePrecision]], N[(x - N[(N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.9999999999999997e45 or 1.69999999999999992e-40 < a

   1. Initial program 69.3%

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

   3. Taylor expanded in a around inf 61.8%

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

      1. associate-/l* 73.7%

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

   5. Simplified 73.7%

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

   if -3.9999999999999997e45 < a < 1.69999999999999992e-40

   1. Initial program 63.8%

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

      1. +-commutative 63.8%

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

      2. associate-/l* 75.8%

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

      3. fma-define 75.8%

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

   3. Simplified 75.8%

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

   5. Taylor expanded in t around inf 77.9%

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

      1. associate--l+ 77.9%

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

      2. associate-*r/ 77.9%

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

      3. associate-*r/ 77.9%

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

      4. mul-1-neg 77.9%

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

      5. div-sub 78.8%

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

      6. mul-1-neg 78.8%

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

      7. distribute-lft-out-- 78.8%

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

      8. associate-*r/ 78.8%

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

      9. mul-1-neg 78.8%

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

      10. unsub-neg 78.8%

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

      11. distribute-rgt-out-- 78.8%

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

   7. Simplified 78.8%

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

   8. Taylor expanded in z around inf 75.4%

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

      1. associate-/l* 76.8%

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

   10. Simplified 76.8%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+45} \lor \neg \left(a \leq 1.7 \cdot 10^{-40}\right):\\ \;\;\;\;x - \frac{z - t}{a} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8500000000:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8500000000.0)
   (+ y (* z (/ (- x y) t)))
   (if (<= t 2.5e+27)
     (+ x (/ (* (- y x) z) (- a t)))
     (- y (/ (* x (- a z)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8500000000.0) {
		tmp = y + (z * ((x - y) / t));
	} else if (t <= 2.5e+27) {
		tmp = x + (((y - x) * z) / (a - t));
	} else {
		tmp = y - ((x * (a - z)) / t);
	}
	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 (t <= (-8500000000.0d0)) then
        tmp = y + (z * ((x - y) / t))
    else if (t <= 2.5d+27) then
        tmp = x + (((y - x) * z) / (a - t))
    else
        tmp = y - ((x * (a - z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8500000000.0) {
		tmp = y + (z * ((x - y) / t));
	} else if (t <= 2.5e+27) {
		tmp = x + (((y - x) * z) / (a - t));
	} else {
		tmp = y - ((x * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8500000000.0:
		tmp = y + (z * ((x - y) / t))
	elif t <= 2.5e+27:
		tmp = x + (((y - x) * z) / (a - t))
	else:
		tmp = y - ((x * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8500000000.0)
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	elseif (t <= 2.5e+27)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / Float64(a - t)));
	else
		tmp = Float64(y - Float64(Float64(x * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -8500000000.0)
		tmp = y + (z * ((x - y) / t));
	elseif (t <= 2.5e+27)
		tmp = x + (((y - x) * z) / (a - t));
	else
		tmp = y - ((x * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8500000000.0], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e+27], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(N[(x * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.5e9

   1. Initial program 41.2%

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

      1. +-commutative 41.2%

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

      2. associate-/l* 68.8%

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

      3. fma-define 68.9%

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

   3. Simplified 68.9%

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

   5. Taylor expanded in t around inf 59.6%

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

      1. associate--l+ 59.6%

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

      2. associate-*r/ 59.6%

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

      3. associate-*r/ 59.6%

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

      4. mul-1-neg 59.6%

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

      5. div-sub 59.6%

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

      6. mul-1-neg 59.6%

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

      7. distribute-lft-out-- 59.6%

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

      8. associate-*r/ 59.6%

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

      9. mul-1-neg 59.6%

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

      10. unsub-neg 59.6%

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

      11. distribute-rgt-out-- 59.7%

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

   7. Simplified 59.7%

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

   8. Taylor expanded in z around inf 59.1%

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

      1. associate-/l* 63.3%

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

   10. Simplified 63.3%

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

   if -8.5e9 < t < 2.4999999999999999e27

   1. Initial program 91.7%

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

   3. Taylor expanded in z around inf 86.3%

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

   if 2.4999999999999999e27 < t

   1. Initial program 40.5%

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

      1. +-commutative 40.5%

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

      2. associate-/l* 68.9%

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

      3. fma-define 68.9%

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

   3. Simplified 68.9%

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

   5. Taylor expanded in t around inf 66.8%

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

      1. associate--l+ 66.8%

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

      2. associate-*r/ 66.8%

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

      3. associate-*r/ 66.8%

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

      4. mul-1-neg 66.8%

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

      5. div-sub 66.8%

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

      6. mul-1-neg 66.8%

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

      7. distribute-lft-out-- 66.8%

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

      8. associate-*r/ 66.8%

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

      9. mul-1-neg 66.8%

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

      10. unsub-neg 66.8%

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

      11. distribute-rgt-out-- 67.1%

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

   7. Simplified 67.1%

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

   8. Taylor expanded in y around 0 71.8%

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

      1. mul-1-neg 71.8%

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

      2. distribute-rgt-neg-in 71.8%

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

      3. sub-neg 71.8%

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

      4. distribute-neg-in 71.8%

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

      5. remove-double-neg 71.8%

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

      6. +-commutative 71.8%

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

      7. sub-neg 71.8%

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

   10. Simplified 71.8%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8500000000:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+44}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{-40}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - t}{a} \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.5e+44)
   (+ x (* (- z t) (/ y (- a t))))
   (if (<= a 1.16e-40)
     (+ y (* z (/ (- x y) t)))
     (- x (* (/ (- z t) a) (- x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e+44) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else if (a <= 1.16e-40) {
		tmp = y + (z * ((x - y) / t));
	} else {
		tmp = x - (((z - t) / a) * (x - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.5d+44)) then
        tmp = x + ((z - t) * (y / (a - t)))
    else if (a <= 1.16d-40) then
        tmp = y + (z * ((x - y) / t))
    else
        tmp = x - (((z - t) / a) * (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e+44) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else if (a <= 1.16e-40) {
		tmp = y + (z * ((x - y) / t));
	} else {
		tmp = x - (((z - t) / a) * (x - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.5e+44:
		tmp = x + ((z - t) * (y / (a - t)))
	elif a <= 1.16e-40:
		tmp = y + (z * ((x - y) / t))
	else:
		tmp = x - (((z - t) / a) * (x - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.5e+44)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	elseif (a <= 1.16e-40)
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	else
		tmp = Float64(x - Float64(Float64(Float64(z - t) / a) * Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.5e+44)
		tmp = x + ((z - t) * (y / (a - t)));
	elseif (a <= 1.16e-40)
		tmp = y + (z * ((x - y) / t));
	else
		tmp = x - (((z - t) / a) * (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.5e+44], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.16e-40], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.5e44

   1. Initial program 65.4%

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

   3. Taylor expanded in y around inf 61.1%

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

      1. *-commutative 61.1%

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

      2. *-lft-identity 61.1%

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

      3. times-frac 69.7%

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

      4. /-rgt-identity 69.7%

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

   5. Simplified 69.7%

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

   if -4.5e44 < a < 1.15999999999999991e-40

   1. Initial program 63.8%

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

      1. +-commutative 63.8%

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

      2. associate-/l* 75.8%

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

      3. fma-define 75.8%

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

   3. Simplified 75.8%

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

   5. Taylor expanded in t around inf 77.9%

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

      1. associate--l+ 77.9%

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

      2. associate-*r/ 77.9%

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

      3. associate-*r/ 77.9%

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

      4. mul-1-neg 77.9%

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

      5. div-sub 78.8%

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

      6. mul-1-neg 78.8%

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

      7. distribute-lft-out-- 78.8%

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

      8. associate-*r/ 78.8%

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

      9. mul-1-neg 78.8%

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

      10. unsub-neg 78.8%

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

      11. distribute-rgt-out-- 78.8%

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

   7. Simplified 78.8%

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

   8. Taylor expanded in z around inf 75.4%

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

      1. associate-/l* 76.8%

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

   10. Simplified 76.8%

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

   if 1.15999999999999991e-40 < a

   1. Initial program 71.8%

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

   3. Taylor expanded in a around inf 65.1%

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

      1. associate-/l* 77.4%

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

   5. Simplified 77.4%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+44}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{-40}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - t}{a} \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 68.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+45} \lor \neg \left(a \leq 9.6 \cdot 10^{-41}\right):\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.5e+45) (not (<= a 9.6e-41)))
   (- x (* z (/ (- x y) a)))
   (+ y (* z (/ (- x y) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.5e+45) || !(a <= 9.6e-41)) {
		tmp = x - (z * ((x - y) / a));
	} else {
		tmp = y + (z * ((x - y) / t));
	}
	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 <= (-4.5d+45)) .or. (.not. (a <= 9.6d-41))) then
        tmp = x - (z * ((x - y) / a))
    else
        tmp = y + (z * ((x - y) / t))
    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 <= -4.5e+45) || !(a <= 9.6e-41)) {
		tmp = x - (z * ((x - y) / a));
	} else {
		tmp = y + (z * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.5e+45) or not (a <= 9.6e-41):
		tmp = x - (z * ((x - y) / a))
	else:
		tmp = y + (z * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.5e+45) || !(a <= 9.6e-41))
		tmp = Float64(x - Float64(z * Float64(Float64(x - y) / a)));
	else
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.5e+45) || ~((a <= 9.6e-41)))
		tmp = x - (z * ((x - y) / a));
	else
		tmp = y + (z * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.5e+45], N[Not[LessEqual[a, 9.6e-41]], $MachinePrecision]], N[(x - N[(z * N[(N[(x - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.4999999999999998e45 or 9.60000000000000087e-41 < a

   1. Initial program 69.3%

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

   3. Taylor expanded in t around 0 60.8%

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

      1. associate-/l* 68.0%

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

   5. Simplified 68.0%

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

   if -4.4999999999999998e45 < a < 9.60000000000000087e-41

   1. Initial program 63.8%

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

      1. +-commutative 63.8%

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

      2. associate-/l* 75.8%

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

      3. fma-define 75.8%

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

   3. Simplified 75.8%

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

   5. Taylor expanded in t around inf 77.9%

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

      1. associate--l+ 77.9%

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

      2. associate-*r/ 77.9%

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

      3. associate-*r/ 77.9%

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

      4. mul-1-neg 77.9%

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

      5. div-sub 78.8%

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

      6. mul-1-neg 78.8%

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

      7. distribute-lft-out-- 78.8%

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

      8. associate-*r/ 78.8%

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

      9. mul-1-neg 78.8%

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

      10. unsub-neg 78.8%

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

      11. distribute-rgt-out-- 78.8%

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

   7. Simplified 78.8%

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

   8. Taylor expanded in z around inf 75.4%

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

      1. associate-/l* 76.8%

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

   10. Simplified 76.8%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+45} \lor \neg \left(a \leq 9.6 \cdot 10^{-41}\right):\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 56.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+98}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+31}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.6e+98) y (if (<= t 2.2e+31) (+ x (* y (/ z (- a t)))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.6e+98) {
		tmp = y;
	} else if (t <= 2.2e+31) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.6d+98)) then
        tmp = y
    else if (t <= 2.2d+31) then
        tmp = x + (y * (z / (a - t)))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.6e+98) {
		tmp = y;
	} else if (t <= 2.2e+31) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.6e+98:
		tmp = y
	elif t <= 2.2e+31:
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.6e+98)
		tmp = y;
	elseif (t <= 2.2e+31)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.6e+98)
		tmp = y;
	elseif (t <= 2.2e+31)
		tmp = x + (y * (z / (a - t)));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.6e+98], y, If[LessEqual[t, 2.2e+31], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -4.60000000000000026e98 or 2.2000000000000001e31 < t

   1. Initial program 37.2%

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

      1. +-commutative 37.2%

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

      2. associate-/l* 66.4%

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

      3. fma-define 66.5%

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

   3. Simplified 66.5%

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

   5. Taylor expanded in y around 0 53.0%

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

      1. +-commutative 53.0%

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

      2. +-commutative 53.0%

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

      3. div-sub 53.0%

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

      4. mul-1-neg 53.0%

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

      5. associate-/l* 66.4%

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

      6. distribute-lft-neg-in 66.4%

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

      7. distribute-rgt-in 66.4%

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

      8. sub-neg 66.4%

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

      9. associate-*l/ 37.2%

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

      10. associate-*r/ 63.2%

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

      11. fma-define 63.2%

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

   7. Simplified 63.2%

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

   8. Taylor expanded in t around inf 49.7%

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

   if -4.60000000000000026e98 < t < 2.2000000000000001e31

   1. Initial program 89.3%

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

   3. Taylor expanded in y around inf 67.7%

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

      1. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in z around inf 61.6%

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

      1. associate-/l* 64.5%

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

   8. Simplified 64.5%

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

Alternative 14: 48.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{+33}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.16e+33) y (if (<= t 2.2e+24) (* x (- 1.0 (/ z a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.16e+33) {
		tmp = y;
	} else if (t <= 2.2e+24) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.16d+33)) then
        tmp = y
    else if (t <= 2.2d+24) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.16e+33) {
		tmp = y;
	} else if (t <= 2.2e+24) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.16e+33:
		tmp = y
	elif t <= 2.2e+24:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.16e+33)
		tmp = y;
	elseif (t <= 2.2e+24)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.16e+33)
		tmp = y;
	elseif (t <= 2.2e+24)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.16e+33], y, If[LessEqual[t, 2.2e+24], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -1.16000000000000001e33 or 2.20000000000000002e24 < t

   1. Initial program 40.7%

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

      1. +-commutative 40.7%

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

      2. associate-/l* 69.1%

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

      3. fma-define 69.2%

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

   3. Simplified 69.2%

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

   5. Taylor expanded in y around 0 56.3%

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

      1. +-commutative 56.3%

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

      2. +-commutative 56.3%

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

      3. div-sub 56.3%

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

      4. mul-1-neg 56.3%

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

      5. associate-/l* 69.1%

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

      6. distribute-lft-neg-in 69.1%

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

      7. distribute-rgt-in 69.1%

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

      8. sub-neg 69.1%

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

      9. associate-*l/ 40.7%

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

      10. associate-*r/ 66.3%

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

      11. fma-define 66.3%

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

   7. Simplified 66.3%

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

   8. Taylor expanded in t around inf 48.0%

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

   if -1.16000000000000001e33 < t < 2.20000000000000002e24

   1. Initial program 91.1%

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

      1. +-commutative 91.1%

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

      2. associate-/l* 95.2%

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

      3. fma-define 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in y around 0 61.7%

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

      1. *-rgt-identity 61.7%

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

      2. mul-1-neg 61.7%

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

      3. associate-/l* 67.3%

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

      4. distribute-rgt-neg-in 67.3%

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

      5. mul-1-neg 67.3%

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

      6. distribute-lft-in 67.3%

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

      7. mul-1-neg 67.3%

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

      8. unsub-neg 67.3%

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

   7. Simplified 67.3%

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

   8. Taylor expanded in t around 0 58.9%

      \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 38.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+113}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+55}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.5e+113) x (if (<= a 3.3e+55) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e+113) {
		tmp = x;
	} else if (a <= 3.3e+55) {
		tmp = y;
	} else {
		tmp = 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 <= (-4.5d+113)) then
        tmp = x
    else if (a <= 3.3d+55) then
        tmp = y
    else
        tmp = 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 <= -4.5e+113) {
		tmp = x;
	} else if (a <= 3.3e+55) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.5e+113:
		tmp = x
	elif a <= 3.3e+55:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.5e+113)
		tmp = x;
	elseif (a <= 3.3e+55)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.5e+113)
		tmp = x;
	elseif (a <= 3.3e+55)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.5e+113], x, If[LessEqual[a, 3.3e+55], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -4.5000000000000001e113 or 3.3e55 < a

   1. Initial program 69.7%

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

      1. +-commutative 69.7%

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

      2. associate-/l* 93.4%

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

      3. fma-define 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in a around inf 57.2%

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

   if -4.5000000000000001e113 < a < 3.3e55

   1. Initial program 64.9%

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

      1. +-commutative 64.9%

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

      2. associate-/l* 76.2%

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

      3. fma-define 76.2%

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

   3. Simplified 76.2%

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

   5. Taylor expanded in y around 0 69.3%

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

      1. +-commutative 69.3%

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

      2. +-commutative 69.3%

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

      3. div-sub 69.3%

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

      4. mul-1-neg 69.3%

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

      5. associate-/l* 73.1%

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

      6. distribute-lft-neg-in 73.1%

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

      7. distribute-rgt-in 76.2%

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

      8. sub-neg 76.2%

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

      9. associate-*l/ 64.9%

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

      10. associate-*r/ 72.3%

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

      11. fma-define 72.4%

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

   7. Simplified 72.4%

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

   8. Taylor expanded in t around inf 35.9%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 25.0% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 66.7%

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

   1. +-commutative 66.7%

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

   2. associate-/l* 82.6%

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

   3. fma-define 82.6%

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

3. Simplified 82.6%

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

5. Taylor expanded in a around inf 27.1%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Alternative 17: 2.8% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 66.7%

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

   1. +-commutative 66.7%

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

   2. associate-/l* 82.6%

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

   3. fma-define 82.6%

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

3. Simplified 82.6%

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

5. Taylor expanded in y around 0 41.6%

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

   1. *-rgt-identity 41.6%

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

   2. mul-1-neg 41.6%

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

   3. associate-/l* 48.0%

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

   4. distribute-rgt-neg-in 48.0%

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

   5. mul-1-neg 48.0%

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

   6. distribute-lft-in 48.1%

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

   7. mul-1-neg 48.1%

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

   8. unsub-neg 48.1%

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

7. Simplified 48.1%

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

8. Taylor expanded in t around inf 2.8%

   \[\leadsto x \cdot \left(1 - \color{blue}{1}\right) \]

9. Taylor expanded in x around 0 2.8%

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

Developer Target 1: 86.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024144 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

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

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