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

Percentage Accurate: 68.3% → 90.5%

Time: 18.1s

Alternatives: 19

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: 68.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.85 \cdot 10^{+31} \lor \neg \left(x \leq 5.4 \cdot 10^{-10}\right):\\ \;\;\;\;x \cdot \left(\left(1 - \frac{t}{t - a}\right) + \left(\frac{z}{t - a} - y \cdot \frac{\frac{z - t}{x}}{t - a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{t - z}{t - a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -3.85e+31) (not (<= x 5.4e-10)))
   (*
    x
    (+
     (- 1.0 (/ t (- t a)))
     (- (/ z (- t a)) (* y (/ (/ (- z t) x) (- t a))))))
   (fma (- y x) (/ (- t z) (- t a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -3.85e+31) || !(x <= 5.4e-10)) {
		tmp = x * ((1.0 - (t / (t - a))) + ((z / (t - a)) - (y * (((z - t) / x) / (t - a)))));
	} else {
		tmp = fma((y - x), ((t - z) / (t - a)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -3.85e+31) || !(x <= 5.4e-10))
		tmp = Float64(x * Float64(Float64(1.0 - Float64(t / Float64(t - a))) + Float64(Float64(z / Float64(t - a)) - Float64(y * Float64(Float64(Float64(z - t) / x) / Float64(t - a))))));
	else
		tmp = fma(Float64(y - x), Float64(Float64(t - z) / Float64(t - a)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -3.85e+31], N[Not[LessEqual[x, 5.4e-10]], $MachinePrecision]], N[(x * N[(N[(1.0 - N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.84999999999999984e31 or 5.4e-10 < x

   1. Initial program 56.5%

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

      1. +-commutative 56.5%

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

      2. associate-/l* 77.6%

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

      3. fma-define 77.6%

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

   3. Simplified 77.6%

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

   5. Taylor expanded in x around -inf 75.3%

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

      1. mul-1-neg 75.3%

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

      2. distribute-rgt-neg-in 75.3%

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

      3. +-commutative 75.3%

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

      4. mul-1-neg 75.3%

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

      5. unsub-neg 75.3%

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

      6. associate-/r* 77.4%

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

      7. associate-/l* 87.7%

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

      8. *-lft-identity 87.7%

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

      9. times-frac 90.7%

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

      10. /-rgt-identity 90.7%

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

      11. +-commutative 90.7%

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

   7. Simplified 90.7%

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

   if -3.84999999999999984e31 < x < 5.4e-10

   1. Initial program 81.8%

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

      1. +-commutative 81.8%

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

      2. associate-/l* 93.7%

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

      3. fma-define 93.6%

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

   3. Simplified 93.6%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.85 \cdot 10^{+31} \lor \neg \left(x \leq 5.4 \cdot 10^{-10}\right):\\ \;\;\;\;x \cdot \left(\left(1 - \frac{t}{t - a}\right) + \left(\frac{z}{t - a} - y \cdot \frac{\frac{z - t}{x}}{t - a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{t - z}{t - a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(z - t\right) \cdot \frac{1}{\frac{t - a}{y - x}}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-259}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t\_2 \leq 10^{+305}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- z t) (/ 1.0 (/ (- t a) (- y x))))))
        (t_2 (+ x (/ (* (- y x) (- t z)) (- t a)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e-259)
       t_2
       (if (<= t_2 0.0)
         (- y (/ (* (- y x) (- z a)) t))
         (if (<= t_2 1e+305) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((z - t) * (1.0 / ((t - a) / (y - x))));
	double t_2 = x + (((y - x) * (t - z)) / (t - a));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e-259) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - (((y - x) * (z - a)) / t);
	} else if (t_2 <= 1e+305) {
		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 = x - ((z - t) * (1.0 / ((t - a) / (y - x))));
	double t_2 = x + (((y - x) * (t - z)) / (t - a));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -5e-259) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - (((y - x) * (z - a)) / t);
	} else if (t_2 <= 1e+305) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((z - t) * (1.0 / ((t - a) / (y - x))))
	t_2 = x + (((y - x) * (t - z)) / (t - a))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -5e-259:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y - (((y - x) * (z - a)) / t)
	elif t_2 <= 1e+305:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(z - t) * Float64(1.0 / Float64(Float64(t - a) / Float64(y - x)))))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(t - a)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e-259)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y - Float64(Float64(Float64(y - x) * Float64(z - a)) / t));
	elseif (t_2 <= 1e+305)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((z - t) * (1.0 / ((t - a) / (y - x))));
	t_2 = x + (((y - x) * (t - z)) / (t - a));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -5e-259)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y - (((y - x) * (z - a)) / t);
	elseif (t_2 <= 1e+305)
		tmp = t_2;
	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[(1.0 / N[(N[(t - a), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e-259], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y - N[(N[(N[(y - x), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+305], 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 9.9999999999999994e304 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 40.8%

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

      1. +-commutative 40.8%

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

      2. associate-/l* 86.0%

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

      3. fma-define 86.0%

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

   3. Simplified 86.0%

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

      1. fma-undefine 86.0%

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

      2. associate-/l* 40.8%

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

      3. *-commutative 40.8%

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

      4. associate-/l* 86.1%

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

   6. Applied egg-rr 86.1%

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

      1. clear-num 86.2%

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

      2. inv-pow 86.2%

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

   8. Applied egg-rr 86.2%

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

      1. unpow-1 86.2%

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

   10. Simplified 86.2%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.99999999999999977e-259 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 9.9999999999999994e304

   1. Initial program 95.1%

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

   if -4.99999999999999977e-259 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.3%

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

      1. +-commutative 3.3%

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

      2. associate-/l* 3.3%

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

      3. fma-define 3.3%

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

   3. Simplified 3.3%

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

   5. Taylor expanded in t around inf 99.7%

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

      1. associate--l+ 99.7%

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

      2. associate-*r/ 99.7%

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

      3. associate-*r/ 99.7%

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

      4. mul-1-neg 99.7%

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

      5. div-sub 99.7%

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

      6. mul-1-neg 99.7%

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

      7. distribute-lft-out-- 99.7%

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

      8. associate-*r/ 99.7%

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

      9. mul-1-neg 99.7%

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

      10. unsub-neg 99.7%

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

      11. distribute-rgt-out-- 99.7%

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

   7. Simplified 99.7%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a} \leq -\infty:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{1}{\frac{t - a}{y - x}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a} \leq -5 \cdot 10^{-259}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a} \leq 0:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a} \leq 10^{+305}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{1}{\frac{t - a}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(z - t\right) \cdot \frac{y - x}{t - a}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-259}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t\_2 \leq 10^{+305}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- z t) (/ (- y x) (- t a)))))
        (t_2 (+ x (/ (* (- y x) (- t z)) (- t a)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e-259)
       t_2
       (if (<= t_2 0.0)
         (- y (/ (* (- y x) (- z a)) t))
         (if (<= t_2 1e+305) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((z - t) * ((y - x) / (t - a)));
	double t_2 = x + (((y - x) * (t - z)) / (t - a));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e-259) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - (((y - x) * (z - a)) / t);
	} else if (t_2 <= 1e+305) {
		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 = x - ((z - t) * ((y - x) / (t - a)));
	double t_2 = x + (((y - x) * (t - z)) / (t - a));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -5e-259) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - (((y - x) * (z - a)) / t);
	} else if (t_2 <= 1e+305) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((z - t) * ((y - x) / (t - a)))
	t_2 = x + (((y - x) * (t - z)) / (t - a))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -5e-259:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y - (((y - x) * (z - a)) / t)
	elif t_2 <= 1e+305:
		tmp = t_2
	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(t - a))))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(t - a)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e-259)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y - Float64(Float64(Float64(y - x) * Float64(z - a)) / t));
	elseif (t_2 <= 1e+305)
		tmp = t_2;
	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) / (t - a)));
	t_2 = x + (((y - x) * (t - z)) / (t - a));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -5e-259)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y - (((y - x) * (z - a)) / t);
	elseif (t_2 <= 1e+305)
		tmp = t_2;
	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[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e-259], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y - N[(N[(N[(y - x), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+305], 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 9.9999999999999994e304 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 40.8%

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

      1. +-commutative 40.8%

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

      2. associate-/l* 86.0%

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

      3. fma-define 86.0%

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

   3. Simplified 86.0%

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

      1. fma-undefine 86.0%

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

      2. associate-/l* 40.8%

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

      3. *-commutative 40.8%

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

      4. associate-/l* 86.1%

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

   6. Applied egg-rr 86.1%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.99999999999999977e-259 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 9.9999999999999994e304

   1. Initial program 95.1%

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

   if -4.99999999999999977e-259 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.3%

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

      1. +-commutative 3.3%

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

      2. associate-/l* 3.3%

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

      3. fma-define 3.3%

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

   3. Simplified 3.3%

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

   5. Taylor expanded in t around inf 99.7%

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

      1. associate--l+ 99.7%

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

      2. associate-*r/ 99.7%

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

      3. associate-*r/ 99.7%

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

      4. mul-1-neg 99.7%

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

      5. div-sub 99.7%

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

      6. mul-1-neg 99.7%

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

      7. distribute-lft-out-- 99.7%

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

      8. associate-*r/ 99.7%

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

      9. mul-1-neg 99.7%

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

      10. unsub-neg 99.7%

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

      11. distribute-rgt-out-- 99.7%

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

   7. Simplified 99.7%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a} \leq -\infty:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{y - x}{t - a}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a} \leq -5 \cdot 10^{-259}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a} \leq 0:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a} \leq 10^{+305}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{y - x}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{t - a}\\ t_2 := x \cdot \left(\left(1 - t\_1\right) + \left(\frac{z}{t - a} - y \cdot \frac{\frac{z - t}{x}}{t - a}\right)\right)\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{+24}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-120}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{y - x}{t - a}\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-59}:\\ \;\;\;\;y \cdot \left(\left(\frac{z}{a - t} + \frac{x}{y}\right) + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (- t a)))
        (t_2
         (*
          x
          (+ (- 1.0 t_1) (- (/ z (- t a)) (* y (/ (/ (- z t) x) (- t a))))))))
   (if (<= x -1.1e+24)
     t_2
     (if (<= x -1.2e-120)
       (- x (* (- z t) (/ (- y x) (- t a))))
       (if (<= x 5.8e-59) (* y (+ (+ (/ z (- a t)) (/ x y)) t_1)) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (t - a);
	double t_2 = x * ((1.0 - t_1) + ((z / (t - a)) - (y * (((z - t) / x) / (t - a)))));
	double tmp;
	if (x <= -1.1e+24) {
		tmp = t_2;
	} else if (x <= -1.2e-120) {
		tmp = x - ((z - t) * ((y - x) / (t - a)));
	} else if (x <= 5.8e-59) {
		tmp = y * (((z / (a - t)) + (x / y)) + t_1);
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = t / (t - a)
    t_2 = x * ((1.0d0 - t_1) + ((z / (t - a)) - (y * (((z - t) / x) / (t - a)))))
    if (x <= (-1.1d+24)) then
        tmp = t_2
    else if (x <= (-1.2d-120)) then
        tmp = x - ((z - t) * ((y - x) / (t - a)))
    else if (x <= 5.8d-59) then
        tmp = y * (((z / (a - t)) + (x / y)) + t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (t - a);
	double t_2 = x * ((1.0 - t_1) + ((z / (t - a)) - (y * (((z - t) / x) / (t - a)))));
	double tmp;
	if (x <= -1.1e+24) {
		tmp = t_2;
	} else if (x <= -1.2e-120) {
		tmp = x - ((z - t) * ((y - x) / (t - a)));
	} else if (x <= 5.8e-59) {
		tmp = y * (((z / (a - t)) + (x / y)) + t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (t - a)
	t_2 = x * ((1.0 - t_1) + ((z / (t - a)) - (y * (((z - t) / x) / (t - a)))))
	tmp = 0
	if x <= -1.1e+24:
		tmp = t_2
	elif x <= -1.2e-120:
		tmp = x - ((z - t) * ((y - x) / (t - a)))
	elif x <= 5.8e-59:
		tmp = y * (((z / (a - t)) + (x / y)) + t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(t - a))
	t_2 = Float64(x * Float64(Float64(1.0 - t_1) + Float64(Float64(z / Float64(t - a)) - Float64(y * Float64(Float64(Float64(z - t) / x) / Float64(t - a))))))
	tmp = 0.0
	if (x <= -1.1e+24)
		tmp = t_2;
	elseif (x <= -1.2e-120)
		tmp = Float64(x - Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(t - a))));
	elseif (x <= 5.8e-59)
		tmp = Float64(y * Float64(Float64(Float64(z / Float64(a - t)) + Float64(x / y)) + t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (t - a);
	t_2 = x * ((1.0 - t_1) + ((z / (t - a)) - (y * (((z - t) / x) / (t - a)))));
	tmp = 0.0;
	if (x <= -1.1e+24)
		tmp = t_2;
	elseif (x <= -1.2e-120)
		tmp = x - ((z - t) * ((y - x) / (t - a)));
	elseif (x <= 5.8e-59)
		tmp = y * (((z / (a - t)) + (x / y)) + t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(1.0 - t$95$1), $MachinePrecision] + N[(N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.1e+24], t$95$2, If[LessEqual[x, -1.2e-120], N[(x - N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e-59], N[(y * N[(N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.10000000000000001e24 or 5.80000000000000033e-59 < x

   1. Initial program 58.8%

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

      1. +-commutative 58.8%

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

      2. associate-/l* 78.8%

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

      3. fma-define 78.8%

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

   3. Simplified 78.8%

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

   5. Taylor expanded in x around -inf 76.5%

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

      1. mul-1-neg 76.5%

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

      2. distribute-rgt-neg-in 76.5%

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

      3. +-commutative 76.5%

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

      4. mul-1-neg 76.5%

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

      5. unsub-neg 76.5%

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

      6. associate-/r* 78.5%

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

      7. associate-/l* 88.4%

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

      8. *-lft-identity 88.4%

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

      9. times-frac 91.2%

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

      10. /-rgt-identity 91.2%

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

      11. +-commutative 91.2%

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

   7. Simplified 91.2%

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

   if -1.10000000000000001e24 < x < -1.2e-120

   1. Initial program 79.7%

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

      1. +-commutative 79.7%

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

      2. associate-/l* 94.6%

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

      3. fma-define 94.6%

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

   3. Simplified 94.6%

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

      1. fma-undefine 94.6%

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

      2. associate-/l* 79.7%

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

      3. *-commutative 79.7%

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

      4. associate-/l* 94.6%

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

   6. Applied egg-rr 94.6%

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

   if -1.2e-120 < x < 5.80000000000000033e-59

   1. Initial program 81.2%

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

   3. Taylor expanded in y around inf 77.8%

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

      1. *-commutative 77.8%

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

      2. *-lft-identity 77.8%

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

      3. times-frac 80.6%

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

      4. /-rgt-identity 80.6%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in y around inf 90.1%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(\left(1 - \frac{t}{t - a}\right) + \left(\frac{z}{t - a} - y \cdot \frac{\frac{z - t}{x}}{t - a}\right)\right)\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-120}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{y - x}{t - a}\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-59}:\\ \;\;\;\;y \cdot \left(\left(\frac{z}{a - t} + \frac{x}{y}\right) + \frac{t}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(1 - \frac{t}{t - a}\right) + \left(\frac{z}{t - a} - y \cdot \frac{\frac{z - t}{x}}{t - a}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 38.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{a - t} \cdot y\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+70}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.96 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ z (- a t)) y)))
   (if (<= t -5.2e+70)
     y
     (if (<= t -1.96e-10)
       t_1
       (if (<= t 1.5e-69) x (if (<= t 4.4e+54) t_1 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z / (a - t)) * y;
	double tmp;
	if (t <= -5.2e+70) {
		tmp = y;
	} else if (t <= -1.96e-10) {
		tmp = t_1;
	} else if (t <= 1.5e-69) {
		tmp = x;
	} else if (t <= 4.4e+54) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (z / (a - t)) * y
    if (t <= (-5.2d+70)) then
        tmp = y
    else if (t <= (-1.96d-10)) then
        tmp = t_1
    else if (t <= 1.5d-69) then
        tmp = x
    else if (t <= 4.4d+54) then
        tmp = t_1
    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 t_1 = (z / (a - t)) * y;
	double tmp;
	if (t <= -5.2e+70) {
		tmp = y;
	} else if (t <= -1.96e-10) {
		tmp = t_1;
	} else if (t <= 1.5e-69) {
		tmp = x;
	} else if (t <= 4.4e+54) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z / (a - t)) * y
	tmp = 0
	if t <= -5.2e+70:
		tmp = y
	elif t <= -1.96e-10:
		tmp = t_1
	elif t <= 1.5e-69:
		tmp = x
	elif t <= 4.4e+54:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z / Float64(a - t)) * y)
	tmp = 0.0
	if (t <= -5.2e+70)
		tmp = y;
	elseif (t <= -1.96e-10)
		tmp = t_1;
	elseif (t <= 1.5e-69)
		tmp = x;
	elseif (t <= 4.4e+54)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z / (a - t)) * y;
	tmp = 0.0;
	if (t <= -5.2e+70)
		tmp = y;
	elseif (t <= -1.96e-10)
		tmp = t_1;
	elseif (t <= 1.5e-69)
		tmp = x;
	elseif (t <= 4.4e+54)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t, -5.2e+70], y, If[LessEqual[t, -1.96e-10], t$95$1, If[LessEqual[t, 1.5e-69], x, If[LessEqual[t, 4.4e+54], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.2000000000000001e70 or 4.3999999999999998e54 < t

   1. Initial program 40.1%

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

      1. +-commutative 40.1%

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

      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 y around 0 60.3%

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

      1. +-commutative 60.3%

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

      2. +-commutative 60.3%

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

      3. div-sub 60.4%

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

      4. mul-1-neg 60.4%

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

      5. associate-/l* 75.8%

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

      6. distribute-lft-neg-in 75.8%

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

      7. distribute-rgt-in 75.8%

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

      8. sub-neg 75.8%

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

      9. associate-*l/ 40.1%

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

      10. associate-*r/ 67.0%

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

      11. fma-define 67.1%

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

   7. Simplified 67.1%

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

   8. Taylor expanded in t around inf 54.1%

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

   if -5.2000000000000001e70 < t < -1.96e-10 or 1.49999999999999995e-69 < t < 4.3999999999999998e54

   1. Initial program 77.0%

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

   3. Taylor expanded in y around inf 63.1%

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

      1. *-commutative 63.1%

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

      2. *-lft-identity 63.1%

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

      3. times-frac 65.2%

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

      4. /-rgt-identity 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in y around inf 64.9%

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

   7. Taylor expanded in z around inf 36.1%

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

      1. associate-*r/ 38.0%

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

      2. *-commutative 38.0%

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

   9. Simplified 38.0%

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

   if -1.96e-10 < t < 1.49999999999999995e-69

   1. Initial program 93.4%

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

      1. +-commutative 93.4%

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

      2. associate-/l* 95.6%

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

      3. fma-define 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in a around inf 46.9%

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

Alternative 6: 65.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - z}{t - a}\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-91}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+66}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t z) (- t a)))))
   (if (<= t -1.7e-40)
     t_1
     (if (<= t 4.2e-91)
       (+ x (* z (/ (- y x) a)))
       (if (<= t 1.05e+66) (* z (/ (- x y) (- t a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / (t - a));
	double tmp;
	if (t <= -1.7e-40) {
		tmp = t_1;
	} else if (t <= 4.2e-91) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 1.05e+66) {
		tmp = z * ((x - y) / (t - 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 * ((t - z) / (t - a))
    if (t <= (-1.7d-40)) then
        tmp = t_1
    else if (t <= 4.2d-91) then
        tmp = x + (z * ((y - x) / a))
    else if (t <= 1.05d+66) then
        tmp = z * ((x - y) / (t - 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 * ((t - z) / (t - a));
	double tmp;
	if (t <= -1.7e-40) {
		tmp = t_1;
	} else if (t <= 4.2e-91) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 1.05e+66) {
		tmp = z * ((x - y) / (t - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - z) / (t - a))
	tmp = 0
	if t <= -1.7e-40:
		tmp = t_1
	elif t <= 4.2e-91:
		tmp = x + (z * ((y - x) / a))
	elif t <= 1.05e+66:
		tmp = z * ((x - y) / (t - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - z) / Float64(t - a)))
	tmp = 0.0
	if (t <= -1.7e-40)
		tmp = t_1;
	elseif (t <= 4.2e-91)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif (t <= 1.05e+66)
		tmp = Float64(z * Float64(Float64(x - y) / Float64(t - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - z) / (t - a));
	tmp = 0.0;
	if (t <= -1.7e-40)
		tmp = t_1;
	elseif (t <= 4.2e-91)
		tmp = x + (z * ((y - x) / a));
	elseif (t <= 1.05e+66)
		tmp = z * ((x - y) / (t - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e-40], t$95$1, If[LessEqual[t, 4.2e-91], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+66], N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.69999999999999992e-40 or 1.05000000000000003e66 < t

   1. Initial program 46.9%

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

      1. +-commutative 46.9%

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

      2. associate-/l* 77.7%

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

      3. fma-define 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in y around 0 62.7%

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

      1. +-commutative 62.7%

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

      2. +-commutative 62.7%

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

      3. div-sub 62.7%

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

      4. mul-1-neg 62.7%

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

      5. associate-/l* 77.7%

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

      6. distribute-lft-neg-in 77.7%

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

      7. distribute-rgt-in 77.7%

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

      8. sub-neg 77.7%

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

      9. associate-*l/ 46.9%

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

      10. associate-*r/ 70.5%

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

      11. fma-define 70.7%

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

   7. Simplified 70.7%

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

   8. Taylor expanded in y around inf 65.6%

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

      1. div-sub 65.6%

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

   10. Simplified 65.6%

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

   if -1.69999999999999992e-40 < t < 4.1999999999999998e-91

   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 t around 0 75.3%

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

      1. associate-/l* 78.2%

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

   5. Simplified 78.2%

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

   if 4.1999999999999998e-91 < t < 1.05000000000000003e66

   1. Initial program 79.7%

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

      1. +-commutative 79.7%

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

      2. associate-/l* 85.6%

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

      3. fma-define 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in y around 0 79.8%

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

      1. +-commutative 79.8%

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

      2. +-commutative 79.8%

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

      3. div-sub 79.8%

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

      4. mul-1-neg 79.8%

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

      5. associate-/l* 79.8%

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

      6. distribute-lft-neg-in 79.8%

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

      7. distribute-rgt-in 85.6%

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

      8. sub-neg 85.6%

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

      9. associate-*l/ 79.7%

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

      10. associate-*r/ 79.9%

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

      11. fma-define 80.1%

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

   7. Simplified 80.1%

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

   8. Taylor expanded in z around inf 64.1%

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

      1. div-sub 64.1%

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

   10. Simplified 64.1%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \frac{t - z}{t - a}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-91}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+66}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - z}{t - a}\\ \mathbf{if}\;t \leq -3.05 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-91}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+59}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t z) (- t a)))))
   (if (<= t -3.05e-40)
     t_1
     (if (<= t 4.6e-91)
       (+ x (* y (/ (- z t) a)))
       (if (<= t 9e+59) (* z (/ (- x y) (- t a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / (t - a));
	double tmp;
	if (t <= -3.05e-40) {
		tmp = t_1;
	} else if (t <= 4.6e-91) {
		tmp = x + (y * ((z - t) / a));
	} else if (t <= 9e+59) {
		tmp = z * ((x - y) / (t - 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 * ((t - z) / (t - a))
    if (t <= (-3.05d-40)) then
        tmp = t_1
    else if (t <= 4.6d-91) then
        tmp = x + (y * ((z - t) / a))
    else if (t <= 9d+59) then
        tmp = z * ((x - y) / (t - 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 * ((t - z) / (t - a));
	double tmp;
	if (t <= -3.05e-40) {
		tmp = t_1;
	} else if (t <= 4.6e-91) {
		tmp = x + (y * ((z - t) / a));
	} else if (t <= 9e+59) {
		tmp = z * ((x - y) / (t - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - z) / (t - a))
	tmp = 0
	if t <= -3.05e-40:
		tmp = t_1
	elif t <= 4.6e-91:
		tmp = x + (y * ((z - t) / a))
	elif t <= 9e+59:
		tmp = z * ((x - y) / (t - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - z) / Float64(t - a)))
	tmp = 0.0
	if (t <= -3.05e-40)
		tmp = t_1;
	elseif (t <= 4.6e-91)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	elseif (t <= 9e+59)
		tmp = Float64(z * Float64(Float64(x - y) / Float64(t - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - z) / (t - a));
	tmp = 0.0;
	if (t <= -3.05e-40)
		tmp = t_1;
	elseif (t <= 4.6e-91)
		tmp = x + (y * ((z - t) / a));
	elseif (t <= 9e+59)
		tmp = z * ((x - y) / (t - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.05e-40], t$95$1, If[LessEqual[t, 4.6e-91], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+59], N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.0500000000000002e-40 or 8.99999999999999919e59 < t

   1. Initial program 46.9%

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

      1. +-commutative 46.9%

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

      2. associate-/l* 77.7%

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

      3. fma-define 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in y around 0 62.7%

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

      1. +-commutative 62.7%

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

      2. +-commutative 62.7%

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

      3. div-sub 62.7%

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

      4. mul-1-neg 62.7%

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

      5. associate-/l* 77.7%

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

      6. distribute-lft-neg-in 77.7%

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

      7. distribute-rgt-in 77.7%

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

      8. sub-neg 77.7%

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

      9. associate-*l/ 46.9%

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

      10. associate-*r/ 70.5%

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

      11. fma-define 70.7%

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

   7. Simplified 70.7%

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

   8. Taylor expanded in y around inf 65.6%

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

      1. div-sub 65.6%

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

   10. Simplified 65.6%

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

   if -3.0500000000000002e-40 < t < 4.59999999999999991e-91

   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 79.6%

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

      1. *-commutative 79.6%

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

      2. *-lft-identity 79.6%

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

      3. times-frac 77.8%

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

      4. /-rgt-identity 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in a around inf 70.8%

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

      1. associate-/l* 72.0%

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

   8. Simplified 72.0%

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

   if 4.59999999999999991e-91 < t < 8.99999999999999919e59

   1. Initial program 79.7%

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

      1. +-commutative 79.7%

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

      2. associate-/l* 85.6%

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

      3. fma-define 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in y around 0 79.8%

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

      1. +-commutative 79.8%

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

      2. +-commutative 79.8%

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

      3. div-sub 79.8%

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

      4. mul-1-neg 79.8%

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

      5. associate-/l* 79.8%

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

      6. distribute-lft-neg-in 79.8%

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

      7. distribute-rgt-in 85.6%

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

      8. sub-neg 85.6%

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

      9. associate-*l/ 79.7%

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

      10. associate-*r/ 79.9%

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

      11. fma-define 80.1%

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

   7. Simplified 80.1%

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

   8. Taylor expanded in z around inf 64.1%

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

      1. div-sub 64.1%

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

   10. Simplified 64.1%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.05 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \frac{t - z}{t - a}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-91}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+59}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - z}{t - a}\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-91}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t z) (- t a)))))
   (if (<= t -6.5e-40)
     t_1
     (if (<= t 1.2e-91)
       (+ x (/ (* z y) a))
       (if (<= t 1.35e+58) (* z (/ (- x y) (- t a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / (t - a));
	double tmp;
	if (t <= -6.5e-40) {
		tmp = t_1;
	} else if (t <= 1.2e-91) {
		tmp = x + ((z * y) / a);
	} else if (t <= 1.35e+58) {
		tmp = z * ((x - y) / (t - 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 * ((t - z) / (t - a))
    if (t <= (-6.5d-40)) then
        tmp = t_1
    else if (t <= 1.2d-91) then
        tmp = x + ((z * y) / a)
    else if (t <= 1.35d+58) then
        tmp = z * ((x - y) / (t - 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 * ((t - z) / (t - a));
	double tmp;
	if (t <= -6.5e-40) {
		tmp = t_1;
	} else if (t <= 1.2e-91) {
		tmp = x + ((z * y) / a);
	} else if (t <= 1.35e+58) {
		tmp = z * ((x - y) / (t - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - z) / (t - a))
	tmp = 0
	if t <= -6.5e-40:
		tmp = t_1
	elif t <= 1.2e-91:
		tmp = x + ((z * y) / a)
	elif t <= 1.35e+58:
		tmp = z * ((x - y) / (t - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - z) / Float64(t - a)))
	tmp = 0.0
	if (t <= -6.5e-40)
		tmp = t_1;
	elseif (t <= 1.2e-91)
		tmp = Float64(x + Float64(Float64(z * y) / a));
	elseif (t <= 1.35e+58)
		tmp = Float64(z * Float64(Float64(x - y) / Float64(t - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - z) / (t - a));
	tmp = 0.0;
	if (t <= -6.5e-40)
		tmp = t_1;
	elseif (t <= 1.2e-91)
		tmp = x + ((z * y) / a);
	elseif (t <= 1.35e+58)
		tmp = z * ((x - y) / (t - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e-40], t$95$1, If[LessEqual[t, 1.2e-91], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+58], N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.4999999999999999e-40 or 1.3500000000000001e58 < t

   1. Initial program 46.9%

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

      1. +-commutative 46.9%

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

      2. associate-/l* 77.7%

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

      3. fma-define 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in y around 0 62.7%

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

      1. +-commutative 62.7%

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

      2. +-commutative 62.7%

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

      3. div-sub 62.7%

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

      4. mul-1-neg 62.7%

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

      5. associate-/l* 77.7%

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

      6. distribute-lft-neg-in 77.7%

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

      7. distribute-rgt-in 77.7%

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

      8. sub-neg 77.7%

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

      9. associate-*l/ 46.9%

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

      10. associate-*r/ 70.5%

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

      11. fma-define 70.7%

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

   7. Simplified 70.7%

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

   8. Taylor expanded in y around inf 65.6%

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

      1. div-sub 65.6%

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

   10. Simplified 65.6%

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

   if -6.4999999999999999e-40 < t < 1.20000000000000005e-91

   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 79.6%

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

      1. *-commutative 79.6%

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

      2. *-lft-identity 79.6%

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

      3. times-frac 77.8%

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

      4. /-rgt-identity 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in t around 0 68.8%

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

   if 1.20000000000000005e-91 < t < 1.3500000000000001e58

   1. Initial program 79.7%

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

      1. +-commutative 79.7%

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

      2. associate-/l* 85.6%

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

      3. fma-define 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in y around 0 79.8%

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

      1. +-commutative 79.8%

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

      2. +-commutative 79.8%

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

      3. div-sub 79.8%

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

      4. mul-1-neg 79.8%

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

      5. associate-/l* 79.8%

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

      6. distribute-lft-neg-in 79.8%

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

      7. distribute-rgt-in 85.6%

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

      8. sub-neg 85.6%

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

      9. associate-*l/ 79.7%

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

      10. associate-*r/ 79.9%

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

      11. fma-define 80.1%

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

   7. Simplified 80.1%

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

   8. Taylor expanded in z around inf 64.1%

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

      1. div-sub 64.1%

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

   10. Simplified 64.1%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \frac{t - z}{t - a}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-91}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+75}:\\ \;\;\;\;y \cdot \frac{t - z}{t - a}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y - z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.65e+75)
   (* y (/ (- t z) (- t a)))
   (if (<= t 2.1e+35)
     (+ x (/ (* (- y x) (- t z)) (- t a)))
     (- y (* z (/ (- y x) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.65e+75) {
		tmp = y * ((t - z) / (t - a));
	} else if (t <= 2.1e+35) {
		tmp = x + (((y - x) * (t - z)) / (t - a));
	} else {
		tmp = y - (z * ((y - x) / 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 <= (-1.65d+75)) then
        tmp = y * ((t - z) / (t - a))
    else if (t <= 2.1d+35) then
        tmp = x + (((y - x) * (t - z)) / (t - a))
    else
        tmp = y - (z * ((y - x) / 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 <= -1.65e+75) {
		tmp = y * ((t - z) / (t - a));
	} else if (t <= 2.1e+35) {
		tmp = x + (((y - x) * (t - z)) / (t - a));
	} else {
		tmp = y - (z * ((y - x) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.65e+75:
		tmp = y * ((t - z) / (t - a))
	elif t <= 2.1e+35:
		tmp = x + (((y - x) * (t - z)) / (t - a))
	else:
		tmp = y - (z * ((y - x) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.65e+75)
		tmp = Float64(y * Float64(Float64(t - z) / Float64(t - a)));
	elseif (t <= 2.1e+35)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(t - a)));
	else
		tmp = Float64(y - Float64(z * Float64(Float64(y - x) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.65e+75)
		tmp = y * ((t - z) / (t - a));
	elseif (t <= 2.1e+35)
		tmp = x + (((y - x) * (t - z)) / (t - a));
	else
		tmp = y - (z * ((y - x) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.65e+75], N[(y * N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e+35], N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.64999999999999999e75

   1. Initial program 33.9%

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

      1. +-commutative 33.9%

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

      2. associate-/l* 79.6%

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

      3. fma-define 79.6%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in y around 0 57.0%

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

      1. +-commutative 57.0%

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

      2. +-commutative 57.0%

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

      3. div-sub 57.0%

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

      4. mul-1-neg 57.0%

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

      5. associate-/l* 79.6%

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

      6. distribute-lft-neg-in 79.6%

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

      7. distribute-rgt-in 79.6%

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

      8. sub-neg 79.6%

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

      9. associate-*l/ 33.9%

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

      10. associate-*r/ 67.4%

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

      11. fma-define 67.7%

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

   7. Simplified 67.7%

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

   8. Taylor expanded in y around inf 75.8%

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

      1. div-sub 75.8%

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

   10. Simplified 75.8%

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

   if -1.64999999999999999e75 < t < 2.0999999999999999e35

   1. Initial program 90.2%

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

   if 2.0999999999999999e35 < t

   1. Initial program 45.4%

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

      1. +-commutative 45.4%

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

      2. associate-/l* 69.4%

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

      3. fma-define 69.4%

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

   3. Simplified 69.4%

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

   5. Taylor expanded in z around inf 41.7%

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

      1. +-commutative 41.7%

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

      2. mul-1-neg 41.7%

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

      3. unsub-neg 41.7%

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

      4. +-commutative 41.7%

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

      5. associate-/r* 38.7%

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

      6. associate-/l* 51.0%

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

      7. *-lft-identity 51.0%

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

      8. times-frac 57.0%

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

      9. /-rgt-identity 57.0%

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

   7. Simplified 57.0%

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

   8. Taylor expanded in t around -inf 43.4%

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

      1. fma-define 43.4%

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

      2. associate-/l* 43.3%

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

      3. associate-/l* 51.5%

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

      4. mul-1-neg 51.5%

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

   10. Simplified 51.5%

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

   11. Taylor expanded in a around 0 63.6%

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

       1. mul-1-neg 63.6%

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

       2. unsub-neg 63.6%

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

       3. associate-/l* 71.5%

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

   13. Simplified 71.5%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+75}:\\ \;\;\;\;y \cdot \frac{t - z}{t - a}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y - z \cdot \frac{y - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - z}{t}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq 1.46 \cdot 10^{+53}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t z) t))))
   (if (<= t -1.4e-21)
     t_1
     (if (<= t 2.7e-8)
       (+ x (/ (* z y) a))
       (if (<= t 1.46e+53) (* z (/ (- x y) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double tmp;
	if (t <= -1.4e-21) {
		tmp = t_1;
	} else if (t <= 2.7e-8) {
		tmp = x + ((z * y) / a);
	} else if (t <= 1.46e+53) {
		tmp = z * ((x - y) / t);
	} 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 * ((t - z) / t)
    if (t <= (-1.4d-21)) then
        tmp = t_1
    else if (t <= 2.7d-8) then
        tmp = x + ((z * y) / a)
    else if (t <= 1.46d+53) then
        tmp = z * ((x - y) / t)
    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 * ((t - z) / t);
	double tmp;
	if (t <= -1.4e-21) {
		tmp = t_1;
	} else if (t <= 2.7e-8) {
		tmp = x + ((z * y) / a);
	} else if (t <= 1.46e+53) {
		tmp = z * ((x - y) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - z) / t)
	tmp = 0
	if t <= -1.4e-21:
		tmp = t_1
	elif t <= 2.7e-8:
		tmp = x + ((z * y) / a)
	elif t <= 1.46e+53:
		tmp = z * ((x - y) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - z) / t))
	tmp = 0.0
	if (t <= -1.4e-21)
		tmp = t_1;
	elseif (t <= 2.7e-8)
		tmp = Float64(x + Float64(Float64(z * y) / a));
	elseif (t <= 1.46e+53)
		tmp = Float64(z * Float64(Float64(x - y) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - z) / t);
	tmp = 0.0;
	if (t <= -1.4e-21)
		tmp = t_1;
	elseif (t <= 2.7e-8)
		tmp = x + ((z * y) / a);
	elseif (t <= 1.46e+53)
		tmp = z * ((x - y) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e-21], t$95$1, If[LessEqual[t, 2.7e-8], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.46e+53], N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.40000000000000002e-21 or 1.45999999999999999e53 < t

   1. Initial program 46.9%

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

      1. +-commutative 46.9%

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

      2. associate-/l* 77.7%

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

      3. fma-define 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in y around 0 62.7%

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

      1. +-commutative 62.7%

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

      2. +-commutative 62.7%

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

      3. div-sub 62.7%

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

      4. mul-1-neg 62.7%

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

      5. associate-/l* 77.7%

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

      6. distribute-lft-neg-in 77.7%

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

      7. distribute-rgt-in 77.7%

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

      8. sub-neg 77.7%

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

      9. associate-*l/ 46.9%

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

      10. associate-*r/ 70.5%

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

      11. fma-define 70.7%

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

   7. Simplified 70.7%

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

   8. Taylor expanded in y around -inf 40.6%

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

   9. Taylor expanded in a around 0 35.6%

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

       1. mul-1-neg 35.6%

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

       2. associate-/l* 58.2%

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

       3. distribute-lft-neg-in 58.2%

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

   11. Simplified 58.2%

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

   if -1.40000000000000002e-21 < t < 2.70000000000000002e-8

   1. Initial program 93.4%

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

   3. Taylor expanded in y around inf 79.8%

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

      1. *-commutative 79.8%

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

      2. *-lft-identity 79.8%

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

      3. times-frac 77.6%

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

      4. /-rgt-identity 77.6%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in t around 0 66.1%

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

   if 2.70000000000000002e-8 < t < 1.45999999999999999e53

   1. Initial program 57.8%

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

      1. +-commutative 57.8%

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

      2. associate-/l* 72.1%

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

      3. fma-define 72.1%

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

   3. Simplified 72.1%

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

   5. Taylor expanded in z around inf 85.4%

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

      1. +-commutative 85.4%

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

      2. mul-1-neg 85.4%

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

      3. unsub-neg 85.4%

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

      4. +-commutative 85.4%

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

      5. associate-/r* 72.1%

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

      6. associate-/l* 78.3%

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

      7. *-lft-identity 78.3%

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

      8. times-frac 85.4%

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

      9. /-rgt-identity 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in t around -inf 71.5%

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

      1. fma-define 71.5%

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

      2. associate-/l* 71.5%

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

      3. associate-/l* 71.5%

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

      4. mul-1-neg 71.5%

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

   10. Simplified 71.5%

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

   11. Taylor expanded in z around inf 76.2%

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

       1. mul-1-neg 76.2%

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

       2. associate-/l* 76.1%

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

       3. *-commutative 76.1%

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

       4. distribute-lft-neg-in 76.1%

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

       5. mul-1-neg 76.1%

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

       6. associate-*r/ 76.1%

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

       7. neg-mul-1 76.1%

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

   13. Simplified 76.1%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-21}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq 1.46 \cdot 10^{+53}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+71}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -480:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+68}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.06e+71)
   y
   (if (<= t -480.0)
     (* (/ z (- a t)) y)
     (if (<= t 4.4e+68) (+ x (/ (* z y) a)) (+ y (* a (/ y t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.06e+71) {
		tmp = y;
	} else if (t <= -480.0) {
		tmp = (z / (a - t)) * y;
	} else if (t <= 4.4e+68) {
		tmp = x + ((z * y) / a);
	} else {
		tmp = y + (a * (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 (t <= (-1.06d+71)) then
        tmp = y
    else if (t <= (-480.0d0)) then
        tmp = (z / (a - t)) * y
    else if (t <= 4.4d+68) then
        tmp = x + ((z * y) / a)
    else
        tmp = y + (a * (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 (t <= -1.06e+71) {
		tmp = y;
	} else if (t <= -480.0) {
		tmp = (z / (a - t)) * y;
	} else if (t <= 4.4e+68) {
		tmp = x + ((z * y) / a);
	} else {
		tmp = y + (a * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.06e+71:
		tmp = y
	elif t <= -480.0:
		tmp = (z / (a - t)) * y
	elif t <= 4.4e+68:
		tmp = x + ((z * y) / a)
	else:
		tmp = y + (a * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.06e+71)
		tmp = y;
	elseif (t <= -480.0)
		tmp = Float64(Float64(z / Float64(a - t)) * y);
	elseif (t <= 4.4e+68)
		tmp = Float64(x + Float64(Float64(z * y) / a));
	else
		tmp = Float64(y + Float64(a * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.06e+71)
		tmp = y;
	elseif (t <= -480.0)
		tmp = (z / (a - t)) * y;
	elseif (t <= 4.4e+68)
		tmp = x + ((z * y) / a);
	else
		tmp = y + (a * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.06e+71], y, If[LessEqual[t, -480.0], N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 4.4e+68], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(y + N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.06e71

   1. Initial program 35.2%

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

      1. +-commutative 35.2%

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

      2. associate-/l* 80.0%

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

      3. fma-define 80.0%

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

   3. Simplified 80.0%

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

   5. Taylor expanded in y around 0 57.8%

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

      1. +-commutative 57.8%

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

      2. +-commutative 57.8%

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

      3. div-sub 57.8%

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

      4. mul-1-neg 57.8%

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

      5. associate-/l* 80.0%

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

      6. distribute-lft-neg-in 80.0%

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

      7. distribute-rgt-in 80.0%

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

      8. sub-neg 80.0%

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

      9. associate-*l/ 35.2%

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

      10. associate-*r/ 67.9%

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

      11. fma-define 68.3%

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

   7. Simplified 68.3%

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

   8. Taylor expanded in t around inf 62.7%

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

   if -1.06e71 < t < -480

   1. Initial program 78.7%

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

   3. Taylor expanded in y around inf 59.5%

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

      1. *-commutative 59.5%

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

      2. *-lft-identity 59.5%

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

      3. times-frac 64.6%

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

      4. /-rgt-identity 64.6%

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

   5. Simplified 64.6%

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

   6. Taylor expanded in y around inf 64.5%

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

   7. Taylor expanded in z around inf 34.9%

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

      1. associate-*r/ 40.1%

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

      2. *-commutative 40.1%

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

   9. Simplified 40.1%

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

   if -480 < t < 4.39999999999999974e68

   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 75.7%

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

      1. *-commutative 75.7%

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

      2. *-lft-identity 75.7%

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

      3. times-frac 74.5%

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

      4. /-rgt-identity 74.5%

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

   5. Simplified 74.5%

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

   6. Taylor expanded in t around 0 61.1%

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

   if 4.39999999999999974e68 < t

   1. Initial program 44.4%

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

      1. +-commutative 44.4%

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

      2. associate-/l* 70.5%

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

      3. fma-define 70.5%

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

   3. Simplified 70.5%

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

   5. Taylor expanded in z around inf 36.0%

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

      1. +-commutative 36.0%

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

      2. mul-1-neg 36.0%

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

      3. unsub-neg 36.0%

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

      4. +-commutative 36.0%

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

      5. associate-/r* 34.6%

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

      6. associate-/l* 46.8%

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

      7. *-lft-identity 46.8%

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

      8. times-frac 53.9%

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

      9. /-rgt-identity 53.9%

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

   7. Simplified 53.9%

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

   8. Taylor expanded in t around -inf 40.1%

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

      1. fma-define 40.1%

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

      2. associate-/l* 40.0%

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

      3. associate-/l* 49.6%

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

      4. mul-1-neg 49.6%

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

   10. Simplified 49.6%

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

   11. Taylor expanded in z around 0 41.3%

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

       1. associate-/l* 56.9%

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

   13. Simplified 56.9%

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

   14. Taylor expanded in y around inf 34.4%

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

       1. associate-/l* 45.6%

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

   16. Simplified 45.6%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+71}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -480:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+68}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+70}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -24.5:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+66}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.2e+70)
   y
   (if (<= t -24.5)
     (* (/ z (- a t)) y)
     (if (<= t 2.4e+66) (+ x (/ (* z y) a)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.2e+70) {
		tmp = y;
	} else if (t <= -24.5) {
		tmp = (z / (a - t)) * y;
	} else if (t <= 2.4e+66) {
		tmp = x + ((z * 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 <= (-5.2d+70)) then
        tmp = y
    else if (t <= (-24.5d0)) then
        tmp = (z / (a - t)) * y
    else if (t <= 2.4d+66) then
        tmp = x + ((z * 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 <= -5.2e+70) {
		tmp = y;
	} else if (t <= -24.5) {
		tmp = (z / (a - t)) * y;
	} else if (t <= 2.4e+66) {
		tmp = x + ((z * y) / a);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.2e+70:
		tmp = y
	elif t <= -24.5:
		tmp = (z / (a - t)) * y
	elif t <= 2.4e+66:
		tmp = x + ((z * y) / a)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.2e+70)
		tmp = y;
	elseif (t <= -24.5)
		tmp = Float64(Float64(z / Float64(a - t)) * y);
	elseif (t <= 2.4e+66)
		tmp = Float64(x + Float64(Float64(z * y) / a));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.2e+70)
		tmp = y;
	elseif (t <= -24.5)
		tmp = (z / (a - t)) * y;
	elseif (t <= 2.4e+66)
		tmp = x + ((z * y) / a);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.2e+70], y, If[LessEqual[t, -24.5], N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 2.4e+66], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.2000000000000001e70 or 2.4000000000000002e66 < t

   1. Initial program 39.5%

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

      1. +-commutative 39.5%

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

      2. associate-/l* 75.6%

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

      3. fma-define 75.6%

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

   3. Simplified 75.6%

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

   5. Taylor expanded in y around 0 59.9%

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

      1. +-commutative 59.9%

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

      2. +-commutative 59.9%

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

      3. div-sub 59.9%

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

      4. mul-1-neg 59.9%

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

      5. associate-/l* 75.6%

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

      6. distribute-lft-neg-in 75.6%

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

      7. distribute-rgt-in 75.6%

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

      8. sub-neg 75.6%

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

      9. associate-*l/ 39.5%

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

      10. associate-*r/ 66.7%

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

      11. fma-define 66.8%

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

   7. Simplified 66.8%

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

   8. Taylor expanded in t around inf 54.6%

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

   if -5.2000000000000001e70 < t < -24.5

   1. Initial program 78.7%

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

   3. Taylor expanded in y around inf 59.5%

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

      1. *-commutative 59.5%

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

      2. *-lft-identity 59.5%

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

      3. times-frac 64.6%

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

      4. /-rgt-identity 64.6%

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

   5. Simplified 64.6%

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

   6. Taylor expanded in y around inf 64.5%

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

   7. Taylor expanded in z around inf 34.9%

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

      1. associate-*r/ 40.1%

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

      2. *-commutative 40.1%

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

   9. Simplified 40.1%

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

   if -24.5 < t < 2.4000000000000002e66

   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 75.7%

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

      1. *-commutative 75.7%

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

      2. *-lft-identity 75.7%

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

      3. times-frac 74.5%

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

      4. /-rgt-identity 74.5%

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

   5. Simplified 74.5%

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

   6. Taylor expanded in t around 0 61.1%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+70}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -24.5:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+66}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-96} \lor \neg \left(a \leq 6.5 \cdot 10^{-41}\right):\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.85e-96) (not (<= a 6.5e-41)))
   (+ x (* (- t z) (/ y (- t a))))
   (- y (/ (* (- y x) (- z a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.85e-96) || !(a <= 6.5e-41)) {
		tmp = x + ((t - z) * (y / (t - a)));
	} else {
		tmp = y - (((y - x) * (z - a)) / 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 <= (-1.85d-96)) .or. (.not. (a <= 6.5d-41))) then
        tmp = x + ((t - z) * (y / (t - a)))
    else
        tmp = y - (((y - x) * (z - a)) / 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 <= -1.85e-96) || !(a <= 6.5e-41)) {
		tmp = x + ((t - z) * (y / (t - a)));
	} else {
		tmp = y - (((y - x) * (z - a)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.85e-96) or not (a <= 6.5e-41):
		tmp = x + ((t - z) * (y / (t - a)))
	else:
		tmp = y - (((y - x) * (z - a)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.85e-96) || !(a <= 6.5e-41))
		tmp = Float64(x + Float64(Float64(t - z) * Float64(y / Float64(t - a))));
	else
		tmp = Float64(y - Float64(Float64(Float64(y - x) * Float64(z - a)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.85e-96) || ~((a <= 6.5e-41)))
		tmp = x + ((t - z) * (y / (t - a)));
	else
		tmp = y - (((y - x) * (z - a)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.85e-96], N[Not[LessEqual[a, 6.5e-41]], $MachinePrecision]], N[(x + N[(N[(t - z), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(N[(N[(y - x), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.84999999999999993e-96 or 6.5000000000000004e-41 < a

   1. Initial program 69.1%

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

   3. Taylor expanded in y around inf 66.8%

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

      1. *-commutative 66.8%

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

      2. *-lft-identity 66.8%

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

      3. times-frac 73.7%

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

      4. /-rgt-identity 73.7%

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

   5. Simplified 73.7%

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

   if -1.84999999999999993e-96 < a < 6.5000000000000004e-41

   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* 80.7%

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

      3. fma-define 80.7%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in t around inf 86.7%

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

      1. associate--l+ 86.7%

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

      2. associate-*r/ 86.7%

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

      3. associate-*r/ 86.7%

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

      4. mul-1-neg 86.7%

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

      5. div-sub 86.8%

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

      6. mul-1-neg 86.8%

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

      7. distribute-lft-out-- 86.8%

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

      8. associate-*r/ 86.8%

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

      9. mul-1-neg 86.8%

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

      10. unsub-neg 86.8%

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

      11. distribute-rgt-out-- 86.8%

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

   7. Simplified 86.8%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-96} \lor \neg \left(a \leq 6.5 \cdot 10^{-41}\right):\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \frac{t - z}{t - a}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+38}:\\ \;\;\;\;x + z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y - z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.4e+72)
   (* y (/ (- t z) (- t a)))
   (if (<= t 3.6e+38)
     (+ x (* z (/ (- x y) (- t a))))
     (- y (* z (/ (- y x) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.4e+72) {
		tmp = y * ((t - z) / (t - a));
	} else if (t <= 3.6e+38) {
		tmp = x + (z * ((x - y) / (t - a)));
	} else {
		tmp = y - (z * ((y - x) / 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 <= (-5.4d+72)) then
        tmp = y * ((t - z) / (t - a))
    else if (t <= 3.6d+38) then
        tmp = x + (z * ((x - y) / (t - a)))
    else
        tmp = y - (z * ((y - x) / 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 <= -5.4e+72) {
		tmp = y * ((t - z) / (t - a));
	} else if (t <= 3.6e+38) {
		tmp = x + (z * ((x - y) / (t - a)));
	} else {
		tmp = y - (z * ((y - x) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.4e+72:
		tmp = y * ((t - z) / (t - a))
	elif t <= 3.6e+38:
		tmp = x + (z * ((x - y) / (t - a)))
	else:
		tmp = y - (z * ((y - x) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.4e+72)
		tmp = Float64(y * Float64(Float64(t - z) / Float64(t - a)));
	elseif (t <= 3.6e+38)
		tmp = Float64(x + Float64(z * Float64(Float64(x - y) / Float64(t - a))));
	else
		tmp = Float64(y - Float64(z * Float64(Float64(y - x) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.4e+72)
		tmp = y * ((t - z) / (t - a));
	elseif (t <= 3.6e+38)
		tmp = x + (z * ((x - y) / (t - a)));
	else
		tmp = y - (z * ((y - x) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.4e+72], N[(y * N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e+38], N[(x + N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.4000000000000001e72

   1. Initial program 33.9%

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

      1. +-commutative 33.9%

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

      2. associate-/l* 79.6%

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

      3. fma-define 79.6%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in y around 0 57.0%

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

      1. +-commutative 57.0%

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

      2. +-commutative 57.0%

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

      3. div-sub 57.0%

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

      4. mul-1-neg 57.0%

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

      5. associate-/l* 79.6%

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

      6. distribute-lft-neg-in 79.6%

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

      7. distribute-rgt-in 79.6%

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

      8. sub-neg 79.6%

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

      9. associate-*l/ 33.9%

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

      10. associate-*r/ 67.4%

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

      11. fma-define 67.7%

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

   7. Simplified 67.7%

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

   8. Taylor expanded in y around inf 75.8%

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

      1. div-sub 75.8%

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

   10. Simplified 75.8%

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

   if -5.4000000000000001e72 < t < 3.59999999999999969e38

   1. Initial program 89.6%

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

   3. Taylor expanded in z around inf 78.4%

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

      1. associate-/l* 80.9%

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

   5. Simplified 80.9%

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

   if 3.59999999999999969e38 < t

   1. Initial program 46.2%

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

      1. +-commutative 46.2%

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

      2. associate-/l* 68.8%

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

      3. fma-define 68.8%

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

   3. Simplified 68.8%

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

   5. Taylor expanded in z around inf 42.5%

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

      1. +-commutative 42.5%

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

      2. mul-1-neg 42.5%

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

      3. unsub-neg 42.5%

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

      4. +-commutative 42.5%

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

      5. associate-/r* 39.4%

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

      6. associate-/l* 52.0%

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

      7. *-lft-identity 52.0%

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

      8. times-frac 58.1%

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

      9. /-rgt-identity 58.1%

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

   7. Simplified 58.1%

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

   8. Taylor expanded in t around -inf 44.2%

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

      1. fma-define 44.2%

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

      2. associate-/l* 44.1%

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

      3. associate-/l* 52.5%

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

      4. mul-1-neg 52.5%

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

   10. Simplified 52.5%

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

   11. Taylor expanded in a around 0 64.7%

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

       1. mul-1-neg 64.7%

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

       2. unsub-neg 64.7%

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

       3. associate-/l* 72.7%

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

   13. Simplified 72.7%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \frac{t - z}{t - a}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+38}:\\ \;\;\;\;x + z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y - z \cdot \frac{y - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 68.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-12} \lor \neg \left(t \leq 2.75 \cdot 10^{-93}\right):\\ \;\;\;\;y - z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.4e-12) (not (<= t 2.75e-93)))
   (- y (* z (/ (- y x) t)))
   (+ x (* z (/ (- y x) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.4e-12) || !(t <= 2.75e-93)) {
		tmp = y - (z * ((y - x) / t));
	} else {
		tmp = x + (z * ((y - x) / 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 ((t <= (-3.4d-12)) .or. (.not. (t <= 2.75d-93))) then
        tmp = y - (z * ((y - x) / t))
    else
        tmp = x + (z * ((y - x) / 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 ((t <= -3.4e-12) || !(t <= 2.75e-93)) {
		tmp = y - (z * ((y - x) / t));
	} else {
		tmp = x + (z * ((y - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.4e-12) or not (t <= 2.75e-93):
		tmp = y - (z * ((y - x) / t))
	else:
		tmp = x + (z * ((y - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.4e-12) || !(t <= 2.75e-93))
		tmp = Float64(y - Float64(z * Float64(Float64(y - x) / t)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.4e-12) || ~((t <= 2.75e-93)))
		tmp = y - (z * ((y - x) / t));
	else
		tmp = x + (z * ((y - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.4e-12], N[Not[LessEqual[t, 2.75e-93]], $MachinePrecision]], N[(y - N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4000000000000001e-12 or 2.74999999999999984e-93 < t

   1. Initial program 54.4%

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

      1. +-commutative 54.4%

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

      2. associate-/l* 79.6%

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

      3. fma-define 79.6%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in z around inf 48.8%

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

      1. +-commutative 48.8%

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

      2. mul-1-neg 48.8%

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

      3. unsub-neg 48.8%

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

      4. +-commutative 48.8%

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

      5. associate-/r* 46.5%

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

      6. associate-/l* 56.3%

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

      7. *-lft-identity 56.3%

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

      8. times-frac 63.2%

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

      9. /-rgt-identity 63.2%

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

   7. Simplified 63.2%

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

   8. Taylor expanded in t around -inf 44.8%

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

      1. fma-define 44.8%

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

      2. associate-/l* 48.3%

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

      3. associate-/l* 52.4%

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

      4. mul-1-neg 52.4%

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

   10. Simplified 52.4%

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

   11. Taylor expanded in a around 0 64.4%

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

       1. mul-1-neg 64.4%

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

       2. unsub-neg 64.4%

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

       3. associate-/l* 70.3%

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

   13. Simplified 70.3%

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

   if -3.4000000000000001e-12 < t < 2.74999999999999984e-93

   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 t around 0 76.0%

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

      1. associate-/l* 79.0%

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

   5. Simplified 79.0%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-12} \lor \neg \left(t \leq 2.75 \cdot 10^{-93}\right):\\ \;\;\;\;y - z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 59.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{-40} \lor \neg \left(t \leq 3.8 \cdot 10^{-68}\right):\\ \;\;\;\;y \cdot \frac{t - z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7.2e-40) (not (<= t 3.8e-68)))
   (* y (/ (- t z) (- t a)))
   (+ x (/ (* z y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.2e-40) || !(t <= 3.8e-68)) {
		tmp = y * ((t - z) / (t - a));
	} else {
		tmp = x + ((z * 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 ((t <= (-7.2d-40)) .or. (.not. (t <= 3.8d-68))) then
        tmp = y * ((t - z) / (t - a))
    else
        tmp = x + ((z * 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 ((t <= -7.2e-40) || !(t <= 3.8e-68)) {
		tmp = y * ((t - z) / (t - a));
	} else {
		tmp = x + ((z * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7.2e-40) or not (t <= 3.8e-68):
		tmp = y * ((t - z) / (t - a))
	else:
		tmp = x + ((z * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7.2e-40) || !(t <= 3.8e-68))
		tmp = Float64(y * Float64(Float64(t - z) / Float64(t - a)));
	else
		tmp = Float64(x + Float64(Float64(z * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7.2e-40) || ~((t <= 3.8e-68)))
		tmp = y * ((t - z) / (t - a));
	else
		tmp = x + ((z * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7.2e-40], N[Not[LessEqual[t, 3.8e-68]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.2e-40 or 3.80000000000000038e-68 < t

   1. Initial program 53.2%

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

      1. +-commutative 53.2%

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

      2. associate-/l* 79.0%

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

      3. fma-define 79.0%

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

   3. Simplified 79.0%

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

   5. Taylor expanded in y around 0 65.8%

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

      1. +-commutative 65.8%

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

      2. +-commutative 65.8%

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

      3. div-sub 65.8%

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

      4. mul-1-neg 65.8%

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

      5. associate-/l* 77.7%

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

      6. distribute-lft-neg-in 77.7%

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

      7. distribute-rgt-in 79.0%

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

      8. sub-neg 79.0%

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

      9. associate-*l/ 53.2%

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

      10. associate-*r/ 72.7%

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

      11. fma-define 72.9%

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

   7. Simplified 72.9%

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

   8. Taylor expanded in y around inf 63.0%

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

      1. div-sub 63.0%

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

   10. Simplified 63.0%

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

   if -7.2e-40 < t < 3.80000000000000038e-68

   1. Initial program 93.2%

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

   3. Taylor expanded in y around inf 78.4%

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

      1. *-commutative 78.4%

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

      2. *-lft-identity 78.4%

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

      3. times-frac 76.6%

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

      4. /-rgt-identity 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in t around 0 67.9%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{-40} \lor \neg \left(t \leq 3.8 \cdot 10^{-68}\right):\\ \;\;\;\;y \cdot \frac{t - z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 54.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-10} \lor \neg \left(t \leq 7.5 \cdot 10^{-34}\right):\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.7e-10) (not (<= t 7.5e-34)))
   (* y (/ (- t z) t))
   (+ x (/ (* z y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.7e-10) || !(t <= 7.5e-34)) {
		tmp = y * ((t - z) / t);
	} else {
		tmp = x + ((z * 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 ((t <= (-1.7d-10)) .or. (.not. (t <= 7.5d-34))) then
        tmp = y * ((t - z) / t)
    else
        tmp = x + ((z * 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 ((t <= -1.7e-10) || !(t <= 7.5e-34)) {
		tmp = y * ((t - z) / t);
	} else {
		tmp = x + ((z * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.7e-10) or not (t <= 7.5e-34):
		tmp = y * ((t - z) / t)
	else:
		tmp = x + ((z * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.7e-10) || !(t <= 7.5e-34))
		tmp = Float64(y * Float64(Float64(t - z) / t));
	else
		tmp = Float64(x + Float64(Float64(z * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.7e-10) || ~((t <= 7.5e-34)))
		tmp = y * ((t - z) / t);
	else
		tmp = x + ((z * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.7e-10], N[Not[LessEqual[t, 7.5e-34]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.70000000000000007e-10 or 7.5000000000000004e-34 < t

   1. Initial program 49.6%

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

      1. +-commutative 49.6%

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

      2. associate-/l* 77.4%

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

      3. fma-define 77.4%

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

   3. Simplified 77.4%

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

   5. Taylor expanded in y around 0 63.1%

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

      1. +-commutative 63.1%

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

      2. +-commutative 63.1%

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

      3. div-sub 63.1%

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

      4. mul-1-neg 63.1%

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

      5. associate-/l* 76.7%

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

      6. distribute-lft-neg-in 76.7%

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

      7. distribute-rgt-in 77.4%

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

      8. sub-neg 77.4%

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

      9. associate-*l/ 49.6%

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

      10. associate-*r/ 71.2%

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

      11. fma-define 71.4%

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

   7. Simplified 71.4%

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

   8. Taylor expanded in y around -inf 41.4%

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

   9. Taylor expanded in a around 0 36.4%

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

       1. mul-1-neg 36.4%

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

       2. associate-/l* 55.9%

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

       3. distribute-lft-neg-in 55.9%

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

   11. Simplified 55.9%

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

   if -1.70000000000000007e-10 < t < 7.5000000000000004e-34

   1. Initial program 93.9%

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

   3. Taylor expanded in y around inf 79.6%

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

      1. *-commutative 79.6%

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

      2. *-lft-identity 79.6%

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

      3. times-frac 77.3%

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

      4. /-rgt-identity 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in t around 0 66.8%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-10} \lor \neg \left(t \leq 7.5 \cdot 10^{-34}\right):\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 38.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{-11}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.22e-11) y (if (<= t 8.2e+58) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.22e-11) {
		tmp = y;
	} else if (t <= 8.2e+58) {
		tmp = x;
	} 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 <= (-1.22d-11)) then
        tmp = y
    else if (t <= 8.2d+58) then
        tmp = x
    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 <= -1.22e-11) {
		tmp = y;
	} else if (t <= 8.2e+58) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.22e-11:
		tmp = y
	elif t <= 8.2e+58:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.22e-11)
		tmp = y;
	elseif (t <= 8.2e+58)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.22e-11)
		tmp = y;
	elseif (t <= 8.2e+58)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.22e-11], y, If[LessEqual[t, 8.2e+58], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2200000000000001e-11 or 8.2e58 < t

   1. Initial program 46.1%

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

      1. +-commutative 46.1%

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

      2. associate-/l* 77.4%

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

      3. fma-define 77.4%

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

   3. Simplified 77.4%

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

   5. Taylor expanded in y around 0 62.1%

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

      1. +-commutative 62.1%

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

      2. +-commutative 62.1%

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

      3. div-sub 62.1%

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

      4. mul-1-neg 62.1%

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

      5. associate-/l* 77.4%

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

      6. distribute-lft-neg-in 77.4%

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

      7. distribute-rgt-in 77.4%

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

      8. sub-neg 77.4%

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

      9. associate-*l/ 46.1%

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

      10. associate-*r/ 70.0%

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

      11. fma-define 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in t around inf 47.0%

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

   if -1.2200000000000001e-11 < t < 8.2e58

   1. Initial program 89.8%

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

      1. +-commutative 89.8%

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

      2. associate-/l* 93.0%

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

      3. fma-define 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in a around inf 42.1%

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

Alternative 19: 25.5% 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 69.3%

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

   1. +-commutative 69.3%

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

   2. associate-/l* 85.7%

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

   3. fma-define 85.7%

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

3. Simplified 85.7%

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

5. Taylor expanded in a around inf 27.6%

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

Developer Target 1: 86.4% 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 2024137 
(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))))