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

Percentage Accurate: 68.2% → 90.6%

Time: 15.6s

Alternatives: 21

Speedup: 0.6×

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: 68.2% 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: 90.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-265} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(a - z\right) \cdot \left(x - y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- x y) (- t z)) (- a t)))))
   (if (or (<= t_1 -1e-265) (not (<= t_1 0.0)))
     (fma (- y x) (/ (- z t) (- a t)) x)
     (- y (/ (* (- a z) (- x y)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((x - y) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -1e-265) || !(t_1 <= 0.0)) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else {
		tmp = y - (((a - z) * (x - y)) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(x - y) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -1e-265) || !(t_1 <= 0.0))
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	else
		tmp = Float64(y - Float64(Float64(Float64(a - z) * Float64(x - y)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(x - y), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-265], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y - N[(N[(N[(a - z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.99999999999999985e-266 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 69.1%

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

      1. +-commutative 69.1%

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

      2. associate-/l* 88.0%

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

      3. fma-define 87.9%

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

   3. Simplified 87.9%

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

   if -9.99999999999999985e-266 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.9%

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

      1. +-commutative 3.9%

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

      2. associate-/l* 3.9%

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

      3. fma-define 3.9%

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

   3. Simplified 3.9%

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

   5. Taylor expanded in t around inf 99.6%

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

      1. associate--l+ 99.6%

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

      2. associate-*r/ 99.6%

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

      3. associate-*r/ 99.6%

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

      4. mul-1-neg 99.6%

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

      5. div-sub 99.6%

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

      6. mul-1-neg 99.6%

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

      7. distribute-lft-out-- 99.6%

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

      8. associate-*r/ 99.6%

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

      9. mul-1-neg 99.6%

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

      10. unsub-neg 99.6%

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

      11. distribute-rgt-out-- 99.6%

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

   7. Simplified 99.6%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq -1 \cdot 10^{-265} \lor \neg \left(x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(a - z\right) \cdot \left(x - y\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{t - a}\right)\\ t_2 := x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-205}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-227}:\\ \;\;\;\;y - \frac{\left(a - z\right) \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (* (- y x) (/ -1.0 (- t a))))))
        (t_2 (+ x (/ (* (- x y) (- t z)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e-205)
       t_2
       (if (<= t_2 2e-227) (- y (/ (* (- a z) (- x y)) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) * (-1.0 / (t - a))));
	double t_2 = x + (((x - y) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e-205) {
		tmp = t_2;
	} else if (t_2 <= 2e-227) {
		tmp = y - (((a - z) * (x - y)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) * (-1.0 / (t - a))));
	double t_2 = x + (((x - y) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -5e-205) {
		tmp = t_2;
	} else if (t_2 <= 2e-227) {
		tmp = y - (((a - z) * (x - y)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * ((y - x) * (-1.0 / (t - a))))
	t_2 = x + (((x - y) * (t - z)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -5e-205:
		tmp = t_2
	elif t_2 <= 2e-227:
		tmp = y - (((a - z) * (x - y)) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) * Float64(-1.0 / Float64(t - a)))))
	t_2 = Float64(x + Float64(Float64(Float64(x - y) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e-205)
		tmp = t_2;
	elseif (t_2 <= 2e-227)
		tmp = Float64(y - Float64(Float64(Float64(a - z) * Float64(x - y)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * ((y - x) * (-1.0 / (t - a))));
	t_2 = x + (((x - y) * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -5e-205)
		tmp = t_2;
	elseif (t_2 <= 2e-227)
		tmp = y - (((a - 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[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] * N[(-1.0 / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(x - y), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e-205], t$95$2, If[LessEqual[t$95$2, 2e-227], N[(y - N[(N[(N[(a - z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or 1.99999999999999989e-227 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 57.6%

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

      1. div-inv 57.6%

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

      2. *-commutative 57.6%

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

      3. associate-*l* 84.7%

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

   4. Applied egg-rr 84.7%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -5.00000000000000001e-205

   1. Initial program 96.4%

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

   if -5.00000000000000001e-205 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 1.99999999999999989e-227

   1. Initial program 25.0%

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

      1. +-commutative 25.0%

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

      2. associate-/l* 30.5%

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

      3. fma-define 30.6%

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

   3. Simplified 30.6%

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

   5. Taylor expanded in t around inf 88.5%

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

      1. associate--l+ 88.5%

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

      2. associate-*r/ 88.5%

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

      3. associate-*r/ 88.5%

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

      4. mul-1-neg 88.5%

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

      5. div-sub 88.5%

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

      6. mul-1-neg 88.5%

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

      7. distribute-lft-out-- 88.5%

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

      8. associate-*r/ 88.5%

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

      9. mul-1-neg 88.5%

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

      10. unsub-neg 88.5%

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

      11. distribute-rgt-out-- 88.5%

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

   7. Simplified 88.5%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + \left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{t - a}\right)\\ \mathbf{elif}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq -5 \cdot 10^{-205}:\\ \;\;\;\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq 2 \cdot 10^{-227}:\\ \;\;\;\;y - \frac{\left(a - z\right) \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{t - a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 47.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{+187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ z t)))))
   (if (<= t -3.1e+187)
     t_1
     (if (<= t -2.9e+97)
       (* x (/ (- z a) t))
       (if (<= t 8.5e-33)
         (* x (- 1.0 (/ z a)))
         (if (<= t 5e+15)
           (* y (/ z (- a t)))
           (if (<= t 8e+99) (* x (/ z (- t a))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double tmp;
	if (t <= -3.1e+187) {
		tmp = t_1;
	} else if (t <= -2.9e+97) {
		tmp = x * ((z - a) / t);
	} else if (t <= 8.5e-33) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 5e+15) {
		tmp = y * (z / (a - t));
	} else if (t <= 8e+99) {
		tmp = x * (z / (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 * (1.0d0 - (z / t))
    if (t <= (-3.1d+187)) then
        tmp = t_1
    else if (t <= (-2.9d+97)) then
        tmp = x * ((z - a) / t)
    else if (t <= 8.5d-33) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 5d+15) then
        tmp = y * (z / (a - t))
    else if (t <= 8d+99) then
        tmp = x * (z / (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 * (1.0 - (z / t));
	double tmp;
	if (t <= -3.1e+187) {
		tmp = t_1;
	} else if (t <= -2.9e+97) {
		tmp = x * ((z - a) / t);
	} else if (t <= 8.5e-33) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 5e+15) {
		tmp = y * (z / (a - t));
	} else if (t <= 8e+99) {
		tmp = x * (z / (t - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (z / t))
	tmp = 0
	if t <= -3.1e+187:
		tmp = t_1
	elif t <= -2.9e+97:
		tmp = x * ((z - a) / t)
	elif t <= 8.5e-33:
		tmp = x * (1.0 - (z / a))
	elif t <= 5e+15:
		tmp = y * (z / (a - t))
	elif t <= 8e+99:
		tmp = x * (z / (t - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (t <= -3.1e+187)
		tmp = t_1;
	elseif (t <= -2.9e+97)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= 8.5e-33)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 5e+15)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 8e+99)
		tmp = Float64(x * Float64(z / Float64(t - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (1.0 - (z / t));
	tmp = 0.0;
	if (t <= -3.1e+187)
		tmp = t_1;
	elseif (t <= -2.9e+97)
		tmp = x * ((z - a) / t);
	elseif (t <= 8.5e-33)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 5e+15)
		tmp = y * (z / (a - t));
	elseif (t <= 8e+99)
		tmp = x * (z / (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[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.1e+187], t$95$1, If[LessEqual[t, -2.9e+97], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-33], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+15], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+99], N[(x * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.10000000000000012e187 or 7.9999999999999997e99 < t

   1. Initial program 34.7%

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

      1. +-commutative 34.7%

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

      2. associate-/l* 68.0%

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

      3. fma-define 68.0%

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

   3. Simplified 68.0%

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

   5. Taylor expanded in y around 0 53.3%

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

      1. +-commutative 53.3%

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

      2. +-commutative 53.3%

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

      3. div-sub 53.3%

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

      4. mul-1-neg 53.3%

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

      5. associate-/l* 68.0%

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

      6. distribute-lft-neg-in 68.0%

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

      7. distribute-rgt-in 68.0%

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

      8. sub-neg 68.0%

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

      9. associate-*l/ 34.7%

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

      10. associate-*r/ 63.4%

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

      11. fma-define 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in y around inf 71.6%

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

      1. div-sub 71.6%

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

   10. Simplified 71.6%

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

   11. Taylor expanded in a around 0 68.0%

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

       1. mul-1-neg 68.0%

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

       2. div-sub 68.0%

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

       3. sub-neg 68.0%

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

       4. *-inverses 68.0%

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

       5. metadata-eval 68.0%

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

   13. Simplified 68.0%

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

   if -3.10000000000000012e187 < t < -2.89999999999999987e97

   1. Initial program 21.9%

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

      1. +-commutative 21.9%

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

      2. associate-/l* 56.2%

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

      3. fma-define 56.2%

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

   3. Simplified 56.2%

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

   5. Taylor expanded in y around 0 15.0%

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

      1. *-rgt-identity 15.0%

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

      2. mul-1-neg 15.0%

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

      3. associate-/l* 41.0%

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

      4. distribute-rgt-neg-in 41.0%

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

      5. mul-1-neg 41.0%

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

      6. distribute-lft-in 41.2%

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

      7. mul-1-neg 41.2%

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

      8. unsub-neg 41.2%

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

   7. Simplified 41.2%

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

   8. Taylor expanded in t around inf 65.1%

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

      1. associate-*r/ 65.1%

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

      2. mul-1-neg 65.1%

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

      3. sub-neg 65.1%

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

      4. mul-1-neg 65.1%

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

   10. Simplified 65.1%

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

   if -2.89999999999999987e97 < t < 8.49999999999999945e-33

   1. Initial program 85.1%

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

      1. +-commutative 85.1%

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

      2. associate-/l* 94.3%

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

      3. fma-define 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in y around 0 52.7%

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

      1. *-rgt-identity 52.7%

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

      2. mul-1-neg 52.7%

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

      3. associate-/l* 57.3%

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

      4. distribute-rgt-neg-in 57.3%

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

      5. mul-1-neg 57.3%

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

      6. distribute-lft-in 57.2%

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

      7. mul-1-neg 57.2%

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

      8. unsub-neg 57.2%

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

   7. Simplified 57.2%

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

   8. Taylor expanded in t around 0 51.9%

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

   if 8.49999999999999945e-33 < t < 5e15

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-/l* 87.2%

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

      3. fma-define 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in z around inf 67.0%

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

   6. Taylor expanded in y around inf 54.5%

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

      1. associate-/l* 60.4%

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

   8. Simplified 60.4%

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

   if 5e15 < t < 7.9999999999999997e99

   1. Initial program 76.5%

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

      1. +-commutative 76.5%

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

      2. associate-/l* 93.6%

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

      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

   5. Taylor expanded in z around inf 69.8%

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

   6. Taylor expanded in y around 0 52.3%

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

      1. mul-1-neg 52.3%

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

      2. associate-/l* 63.7%

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

   8. Simplified 63.7%

      \[\leadsto \color{blue}{-x \cdot \frac{z}{a - t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+187}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 46.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.3 \cdot 10^{+187}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.58 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.3e+187)
   y
   (if (<= t -1.58e+97)
     (* x (/ (- z a) t))
     (if (<= t 9.5e-33)
       (* x (- 1.0 (/ z a)))
       (if (<= t 5.5e+16)
         (* y (/ z (- a t)))
         (if (<= t 8.5e+99) (* x (/ z (- t a))) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.3e+187) {
		tmp = y;
	} else if (t <= -1.58e+97) {
		tmp = x * ((z - a) / t);
	} else if (t <= 9.5e-33) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 5.5e+16) {
		tmp = y * (z / (a - t));
	} else if (t <= 8.5e+99) {
		tmp = x * (z / (t - 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 <= (-6.3d+187)) then
        tmp = y
    else if (t <= (-1.58d+97)) then
        tmp = x * ((z - a) / t)
    else if (t <= 9.5d-33) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 5.5d+16) then
        tmp = y * (z / (a - t))
    else if (t <= 8.5d+99) then
        tmp = x * (z / (t - 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 <= -6.3e+187) {
		tmp = y;
	} else if (t <= -1.58e+97) {
		tmp = x * ((z - a) / t);
	} else if (t <= 9.5e-33) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 5.5e+16) {
		tmp = y * (z / (a - t));
	} else if (t <= 8.5e+99) {
		tmp = x * (z / (t - a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.3e+187:
		tmp = y
	elif t <= -1.58e+97:
		tmp = x * ((z - a) / t)
	elif t <= 9.5e-33:
		tmp = x * (1.0 - (z / a))
	elif t <= 5.5e+16:
		tmp = y * (z / (a - t))
	elif t <= 8.5e+99:
		tmp = x * (z / (t - a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.3e+187)
		tmp = y;
	elseif (t <= -1.58e+97)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= 9.5e-33)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 5.5e+16)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 8.5e+99)
		tmp = Float64(x * Float64(z / Float64(t - a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.3e+187)
		tmp = y;
	elseif (t <= -1.58e+97)
		tmp = x * ((z - a) / t);
	elseif (t <= 9.5e-33)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 5.5e+16)
		tmp = y * (z / (a - t));
	elseif (t <= 8.5e+99)
		tmp = x * (z / (t - a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.3e+187], y, If[LessEqual[t, -1.58e+97], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-33], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+16], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+99], N[(x * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -6.30000000000000005e187 or 8.49999999999999984e99 < t

   1. Initial program 34.7%

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

      1. +-commutative 34.7%

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

      2. associate-/l* 68.0%

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

      3. fma-define 68.0%

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

   3. Simplified 68.0%

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

   5. Taylor expanded in y around 0 53.3%

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

      1. +-commutative 53.3%

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

      2. +-commutative 53.3%

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

      3. div-sub 53.3%

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

      4. mul-1-neg 53.3%

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

      5. associate-/l* 68.0%

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

      6. distribute-lft-neg-in 68.0%

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

      7. distribute-rgt-in 68.0%

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

      8. sub-neg 68.0%

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

      9. associate-*l/ 34.7%

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

      10. associate-*r/ 63.4%

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

      11. fma-define 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in t around inf 63.1%

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

   if -6.30000000000000005e187 < t < -1.57999999999999993e97

   1. Initial program 21.9%

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

      1. +-commutative 21.9%

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

      2. associate-/l* 56.2%

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

      3. fma-define 56.2%

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

   3. Simplified 56.2%

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

   5. Taylor expanded in y around 0 15.0%

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

      1. *-rgt-identity 15.0%

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

      2. mul-1-neg 15.0%

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

      3. associate-/l* 41.0%

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

      4. distribute-rgt-neg-in 41.0%

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

      5. mul-1-neg 41.0%

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

      6. distribute-lft-in 41.2%

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

      7. mul-1-neg 41.2%

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

      8. unsub-neg 41.2%

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

   7. Simplified 41.2%

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

   8. Taylor expanded in t around inf 65.1%

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

      1. associate-*r/ 65.1%

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

      2. mul-1-neg 65.1%

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

      3. sub-neg 65.1%

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

      4. mul-1-neg 65.1%

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

   10. Simplified 65.1%

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

   if -1.57999999999999993e97 < t < 9.50000000000000019e-33

   1. Initial program 85.1%

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

      1. +-commutative 85.1%

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

      2. associate-/l* 94.3%

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

      3. fma-define 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in y around 0 52.7%

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

      1. *-rgt-identity 52.7%

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

      2. mul-1-neg 52.7%

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

      3. associate-/l* 57.3%

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

      4. distribute-rgt-neg-in 57.3%

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

      5. mul-1-neg 57.3%

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

      6. distribute-lft-in 57.2%

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

      7. mul-1-neg 57.2%

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

      8. unsub-neg 57.2%

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

   7. Simplified 57.2%

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

   8. Taylor expanded in t around 0 51.9%

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

   if 9.50000000000000019e-33 < t < 5.5e16

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-/l* 87.2%

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

      3. fma-define 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in z around inf 67.0%

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

   6. Taylor expanded in y around inf 54.5%

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

      1. associate-/l* 60.4%

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

   8. Simplified 60.4%

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

   if 5.5e16 < t < 8.49999999999999984e99

   1. Initial program 76.5%

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

      1. +-commutative 76.5%

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

      2. associate-/l* 93.6%

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

      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

   5. Taylor expanded in z around inf 69.8%

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

   6. Taylor expanded in y around 0 52.3%

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

      1. mul-1-neg 52.3%

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

      2. associate-/l* 63.7%

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

   8. Simplified 63.7%

      \[\leadsto \color{blue}{-x \cdot \frac{z}{a - t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.3 \cdot 10^{+187}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.58 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 46.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+187}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 10^{-32}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.1e+187)
   y
   (if (<= t 1e-32)
     (* x (- 1.0 (/ z a)))
     (if (<= t 3.3e+15)
       (* y (/ z (- a t)))
       (if (<= t 8.2e+99) (* x (/ z (- t a))) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.1e+187) {
		tmp = y;
	} else if (t <= 1e-32) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 3.3e+15) {
		tmp = y * (z / (a - t));
	} else if (t <= 8.2e+99) {
		tmp = x * (z / (t - 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 <= (-3.1d+187)) then
        tmp = y
    else if (t <= 1d-32) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 3.3d+15) then
        tmp = y * (z / (a - t))
    else if (t <= 8.2d+99) then
        tmp = x * (z / (t - 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 <= -3.1e+187) {
		tmp = y;
	} else if (t <= 1e-32) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 3.3e+15) {
		tmp = y * (z / (a - t));
	} else if (t <= 8.2e+99) {
		tmp = x * (z / (t - a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.1e+187:
		tmp = y
	elif t <= 1e-32:
		tmp = x * (1.0 - (z / a))
	elif t <= 3.3e+15:
		tmp = y * (z / (a - t))
	elif t <= 8.2e+99:
		tmp = x * (z / (t - a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.1e+187)
		tmp = y;
	elseif (t <= 1e-32)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 3.3e+15)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 8.2e+99)
		tmp = Float64(x * Float64(z / Float64(t - a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.1e+187)
		tmp = y;
	elseif (t <= 1e-32)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 3.3e+15)
		tmp = y * (z / (a - t));
	elseif (t <= 8.2e+99)
		tmp = x * (z / (t - a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.1e+187], y, If[LessEqual[t, 1e-32], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e+15], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e+99], N[(x * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.10000000000000012e187 or 8.19999999999999959e99 < t

   1. Initial program 34.7%

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

      1. +-commutative 34.7%

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

      2. associate-/l* 68.0%

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

      3. fma-define 68.0%

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

   3. Simplified 68.0%

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

   5. Taylor expanded in y around 0 53.3%

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

      1. +-commutative 53.3%

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

      2. +-commutative 53.3%

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

      3. div-sub 53.3%

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

      4. mul-1-neg 53.3%

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

      5. associate-/l* 68.0%

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

      6. distribute-lft-neg-in 68.0%

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

      7. distribute-rgt-in 68.0%

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

      8. sub-neg 68.0%

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

      9. associate-*l/ 34.7%

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

      10. associate-*r/ 63.4%

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

      11. fma-define 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in t around inf 63.1%

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

   if -3.10000000000000012e187 < t < 1.00000000000000006e-32

   1. Initial program 79.1%

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

      1. +-commutative 79.1%

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

      2. associate-/l* 90.7%

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

      3. fma-define 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in y around 0 49.2%

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

      1. *-rgt-identity 49.2%

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

      2. mul-1-neg 49.2%

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

      3. associate-/l* 55.8%

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

      4. distribute-rgt-neg-in 55.8%

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

      5. mul-1-neg 55.8%

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

      6. distribute-lft-in 55.7%

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

      7. mul-1-neg 55.7%

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

      8. unsub-neg 55.7%

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

   7. Simplified 55.7%

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

   8. Taylor expanded in t around 0 48.8%

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

   if 1.00000000000000006e-32 < t < 3.3e15

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-/l* 87.2%

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

      3. fma-define 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in z around inf 67.0%

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

   6. Taylor expanded in y around inf 54.5%

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

      1. associate-/l* 60.4%

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

   8. Simplified 60.4%

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

   if 3.3e15 < t < 8.19999999999999959e99

   1. Initial program 76.5%

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

      1. +-commutative 76.5%

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

      2. associate-/l* 93.6%

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

      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

   5. Taylor expanded in z around inf 69.8%

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

   6. Taylor expanded in y around 0 52.3%

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

      1. mul-1-neg 52.3%

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

      2. associate-/l* 63.7%

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

   8. Simplified 63.7%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+187}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 10^{-32}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{\left(a - z\right) \cdot \left(x - y\right)}{t}\\ \mathbf{if}\;t \leq -9.6 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9.4 \cdot 10^{-147}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 10^{+75}:\\ \;\;\;\;x + z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (/ (* (- a z) (- x y)) t))))
   (if (<= t -9.6e+94)
     t_1
     (if (<= t -9.4e-147)
       (+ x (* (- z t) (/ y (- a t))))
       (if (<= t 1e+75) (+ x (* z (/ (- x y) (- t a)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (((a - z) * (x - y)) / t);
	double tmp;
	if (t <= -9.6e+94) {
		tmp = t_1;
	} else if (t <= -9.4e-147) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else if (t <= 1e+75) {
		tmp = x + (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 - (((a - z) * (x - y)) / t)
    if (t <= (-9.6d+94)) then
        tmp = t_1
    else if (t <= (-9.4d-147)) then
        tmp = x + ((z - t) * (y / (a - t)))
    else if (t <= 1d+75) then
        tmp = x + (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 - (((a - z) * (x - y)) / t);
	double tmp;
	if (t <= -9.6e+94) {
		tmp = t_1;
	} else if (t <= -9.4e-147) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else if (t <= 1e+75) {
		tmp = x + (z * ((x - y) / (t - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (((a - z) * (x - y)) / t)
	tmp = 0
	if t <= -9.6e+94:
		tmp = t_1
	elif t <= -9.4e-147:
		tmp = x + ((z - t) * (y / (a - t)))
	elif t <= 1e+75:
		tmp = x + (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(Float64(a - z) * Float64(x - y)) / t))
	tmp = 0.0
	if (t <= -9.6e+94)
		tmp = t_1;
	elseif (t <= -9.4e-147)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	elseif (t <= 1e+75)
		tmp = Float64(x + 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 - (((a - z) * (x - y)) / t);
	tmp = 0.0;
	if (t <= -9.6e+94)
		tmp = t_1;
	elseif (t <= -9.4e-147)
		tmp = x + ((z - t) * (y / (a - t)));
	elseif (t <= 1e+75)
		tmp = x + (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[(N[(a - z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.6e+94], t$95$1, If[LessEqual[t, -9.4e-147], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+75], N[(x + N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.5999999999999993e94 or 9.99999999999999927e74 < t

   1. Initial program 34.4%

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

      1. +-commutative 34.4%

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

      2. associate-/l* 66.9%

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

      3. fma-define 66.9%

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

   3. Simplified 66.9%

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

   5. Taylor expanded in t around inf 70.1%

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

      1. associate--l+ 70.1%

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

      2. associate-*r/ 70.1%

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

      3. associate-*r/ 70.1%

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

      4. mul-1-neg 70.1%

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

      5. div-sub 70.1%

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

      6. mul-1-neg 70.1%

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

      7. distribute-lft-out-- 70.1%

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

      8. associate-*r/ 70.1%

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

      9. mul-1-neg 70.1%

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

      10. unsub-neg 70.1%

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

      11. distribute-rgt-out-- 70.3%

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

   7. Simplified 70.3%

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

   if -9.5999999999999993e94 < t < -9.39999999999999978e-147

   1. Initial program 76.1%

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

   3. Taylor expanded in y around inf 74.0%

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

      1. *-commutative 74.0%

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

      2. *-lft-identity 74.0%

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

      3. times-frac 78.7%

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

      4. /-rgt-identity 78.7%

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

   5. Simplified 78.7%

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

   if -9.39999999999999978e-147 < t < 9.99999999999999927e74

   1. Initial program 87.2%

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

   3. Taylor expanded in z around inf 79.7%

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

      1. associate-/l* 86.9%

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

   5. Simplified 86.9%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{+94}:\\ \;\;\;\;y - \frac{\left(a - z\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t \leq -9.4 \cdot 10^{-147}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 10^{+75}:\\ \;\;\;\;x + z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(a - z\right) \cdot \left(x - y\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + a \cdot \frac{y - x}{t}\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-146}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+99}:\\ \;\;\;\;x + z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* a (/ (- y x) t)))))
   (if (<= t -2.2e+95)
     t_1
     (if (<= t -1.15e-146)
       (+ x (* (- z t) (/ y (- a t))))
       (if (<= t 8.2e+99) (+ x (* z (/ (- x y) (- t a)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (a * ((y - x) / t));
	double tmp;
	if (t <= -2.2e+95) {
		tmp = t_1;
	} else if (t <= -1.15e-146) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else if (t <= 8.2e+99) {
		tmp = x + (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 + (a * ((y - x) / t))
    if (t <= (-2.2d+95)) then
        tmp = t_1
    else if (t <= (-1.15d-146)) then
        tmp = x + ((z - t) * (y / (a - t)))
    else if (t <= 8.2d+99) then
        tmp = x + (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 + (a * ((y - x) / t));
	double tmp;
	if (t <= -2.2e+95) {
		tmp = t_1;
	} else if (t <= -1.15e-146) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else if (t <= 8.2e+99) {
		tmp = x + (z * ((x - y) / (t - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (a * ((y - x) / t))
	tmp = 0
	if t <= -2.2e+95:
		tmp = t_1
	elif t <= -1.15e-146:
		tmp = x + ((z - t) * (y / (a - t)))
	elif t <= 8.2e+99:
		tmp = x + (z * ((x - y) / (t - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(a * Float64(Float64(y - x) / t)))
	tmp = 0.0
	if (t <= -2.2e+95)
		tmp = t_1;
	elseif (t <= -1.15e-146)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	elseif (t <= 8.2e+99)
		tmp = Float64(x + 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 + (a * ((y - x) / t));
	tmp = 0.0;
	if (t <= -2.2e+95)
		tmp = t_1;
	elseif (t <= -1.15e-146)
		tmp = x + ((z - t) * (y / (a - t)));
	elseif (t <= 8.2e+99)
		tmp = x + (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[(a * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e+95], t$95$1, If[LessEqual[t, -1.15e-146], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e+99], N[(x + N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1999999999999999e95 or 8.19999999999999959e99 < t

   1. Initial program 32.5%

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

      1. +-commutative 32.5%

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

      2. associate-/l* 66.5%

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

      3. fma-define 66.5%

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

   3. Simplified 66.5%

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

   5. Taylor expanded in z around inf 53.9%

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

      1. +-commutative 53.9%

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

      2. mul-1-neg 53.9%

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

      3. unsub-neg 53.9%

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

   7. Simplified 53.9%

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

   8. Taylor expanded in t around inf 58.2%

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

   9. Taylor expanded in z around 0 63.6%

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

       1. associate-/l* 66.9%

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

   11. Simplified 66.9%

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

   if -2.1999999999999999e95 < t < -1.15e-146

   1. Initial program 76.1%

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

   3. Taylor expanded in y around inf 74.0%

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

      1. *-commutative 74.0%

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

      2. *-lft-identity 74.0%

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

      3. times-frac 78.7%

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

      4. /-rgt-identity 78.7%

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

   5. Simplified 78.7%

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

   if -1.15e-146 < t < 8.19999999999999959e99

   1. Initial program 86.9%

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

   3. Taylor expanded in z around inf 78.8%

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

      1. associate-/l* 85.8%

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

   5. Simplified 85.8%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+95}:\\ \;\;\;\;y + a \cdot \frac{y - x}{t}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-146}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+99}:\\ \;\;\;\;x + z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot \frac{y - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 34.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+185}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-7}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.7e+185)
   y
   (if (<= t -1.9e-240)
     x
     (if (<= t 2.35e-7) (/ y (/ a z)) (if (<= t 8e+99) (* x (/ z t)) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.7e+185) {
		tmp = y;
	} else if (t <= -1.9e-240) {
		tmp = x;
	} else if (t <= 2.35e-7) {
		tmp = y / (a / z);
	} else if (t <= 8e+99) {
		tmp = x * (z / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.7d+185)) then
        tmp = y
    else if (t <= (-1.9d-240)) then
        tmp = x
    else if (t <= 2.35d-7) then
        tmp = y / (a / z)
    else if (t <= 8d+99) then
        tmp = x * (z / t)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.7e+185) {
		tmp = y;
	} else if (t <= -1.9e-240) {
		tmp = x;
	} else if (t <= 2.35e-7) {
		tmp = y / (a / z);
	} else if (t <= 8e+99) {
		tmp = x * (z / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.7e+185:
		tmp = y
	elif t <= -1.9e-240:
		tmp = x
	elif t <= 2.35e-7:
		tmp = y / (a / z)
	elif t <= 8e+99:
		tmp = x * (z / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.7e+185)
		tmp = y;
	elseif (t <= -1.9e-240)
		tmp = x;
	elseif (t <= 2.35e-7)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 8e+99)
		tmp = Float64(x * Float64(z / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.7e+185)
		tmp = y;
	elseif (t <= -1.9e-240)
		tmp = x;
	elseif (t <= 2.35e-7)
		tmp = y / (a / z);
	elseif (t <= 8e+99)
		tmp = x * (z / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.7e+185], y, If[LessEqual[t, -1.9e-240], x, If[LessEqual[t, 2.35e-7], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+99], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], y]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.70000000000000009e185 or 7.9999999999999997e99 < t

   1. Initial program 34.3%

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

      1. +-commutative 34.3%

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

      2. associate-/l* 68.4%

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

      3. fma-define 68.4%

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

   3. Simplified 68.4%

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

   5. Taylor expanded in y around 0 52.6%

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

      1. +-commutative 52.6%

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

      2. +-commutative 52.6%

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

      3. div-sub 52.6%

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

      4. mul-1-neg 52.6%

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

      5. associate-/l* 68.4%

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

      6. distribute-lft-neg-in 68.4%

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

      7. distribute-rgt-in 68.4%

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

      8. sub-neg 68.4%

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

      9. associate-*l/ 34.3%

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

      10. associate-*r/ 63.9%

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

      11. fma-define 64.0%

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

   7. Simplified 64.0%

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

   8. Taylor expanded in t around inf 62.3%

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

   if -1.70000000000000009e185 < t < -1.89999999999999994e-240

   1. Initial program 70.9%

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

      1. +-commutative 70.9%

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

      2. associate-/l* 85.5%

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

      3. fma-define 85.5%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in a around inf 32.4%

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

   if -1.89999999999999994e-240 < t < 2.35e-7

   1. Initial program 86.8%

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

      1. +-commutative 86.8%

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

      2. associate-/l* 94.7%

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

      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. Taylor expanded in y around 0 85.9%

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

      1. +-commutative 85.9%

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

      2. +-commutative 85.9%

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

      3. div-sub 85.9%

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

      4. mul-1-neg 85.9%

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

      5. associate-/l* 87.9%

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

      6. distribute-lft-neg-in 87.9%

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

      7. distribute-rgt-in 94.7%

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

      8. sub-neg 94.7%

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

      9. associate-*l/ 86.8%

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

      10. associate-*r/ 93.6%

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

      11. fma-define 93.5%

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

   7. Simplified 93.5%

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

   8. Taylor expanded in y around inf 45.3%

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

      1. div-sub 45.3%

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

   10. Simplified 45.3%

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

       1. clear-num 45.2%

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

       2. un-div-inv 46.1%

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

   12. Applied egg-rr 46.1%

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

   13. Taylor expanded in t around 0 40.6%

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

   if 2.35e-7 < t < 7.9999999999999997e99

   1. Initial program 77.1%

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

      1. +-commutative 77.1%

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

      2. associate-/l* 90.1%

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

      3. fma-define 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in y around 0 45.0%

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

      1. *-rgt-identity 45.0%

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

      2. mul-1-neg 45.0%

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

      3. associate-/l* 53.5%

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

      4. distribute-rgt-neg-in 53.5%

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

      5. mul-1-neg 53.5%

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

      6. distribute-lft-in 53.7%

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

      7. mul-1-neg 53.7%

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

      8. unsub-neg 53.7%

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

   7. Simplified 53.7%

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

   8. Taylor expanded in a around 0 41.0%

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

Alternative 9: 34.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+185}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-241}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.7e+185)
   y
   (if (<= t -9.2e-241)
     x
     (if (<= t 7e-7) (* y (/ z a)) (if (<= t 8.2e+99) (* x (/ z t)) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.7e+185) {
		tmp = y;
	} else if (t <= -9.2e-241) {
		tmp = x;
	} else if (t <= 7e-7) {
		tmp = y * (z / a);
	} else if (t <= 8.2e+99) {
		tmp = x * (z / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.7d+185)) then
        tmp = y
    else if (t <= (-9.2d-241)) then
        tmp = x
    else if (t <= 7d-7) then
        tmp = y * (z / a)
    else if (t <= 8.2d+99) then
        tmp = x * (z / t)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.7e+185) {
		tmp = y;
	} else if (t <= -9.2e-241) {
		tmp = x;
	} else if (t <= 7e-7) {
		tmp = y * (z / a);
	} else if (t <= 8.2e+99) {
		tmp = x * (z / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.7e+185:
		tmp = y
	elif t <= -9.2e-241:
		tmp = x
	elif t <= 7e-7:
		tmp = y * (z / a)
	elif t <= 8.2e+99:
		tmp = x * (z / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.7e+185)
		tmp = y;
	elseif (t <= -9.2e-241)
		tmp = x;
	elseif (t <= 7e-7)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 8.2e+99)
		tmp = Float64(x * Float64(z / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.7e+185)
		tmp = y;
	elseif (t <= -9.2e-241)
		tmp = x;
	elseif (t <= 7e-7)
		tmp = y * (z / a);
	elseif (t <= 8.2e+99)
		tmp = x * (z / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.7e+185], y, If[LessEqual[t, -9.2e-241], x, If[LessEqual[t, 7e-7], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e+99], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], y]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.70000000000000009e185 or 8.19999999999999959e99 < t

   1. Initial program 34.3%

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

      1. +-commutative 34.3%

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

      2. associate-/l* 68.4%

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

      3. fma-define 68.4%

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

   3. Simplified 68.4%

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

   5. Taylor expanded in y around 0 52.6%

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

      1. +-commutative 52.6%

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

      2. +-commutative 52.6%

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

      3. div-sub 52.6%

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

      4. mul-1-neg 52.6%

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

      5. associate-/l* 68.4%

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

      6. distribute-lft-neg-in 68.4%

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

      7. distribute-rgt-in 68.4%

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

      8. sub-neg 68.4%

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

      9. associate-*l/ 34.3%

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

      10. associate-*r/ 63.9%

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

      11. fma-define 64.0%

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

   7. Simplified 64.0%

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

   8. Taylor expanded in t around inf 62.3%

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

   if -1.70000000000000009e185 < t < -9.1999999999999997e-241

   1. Initial program 70.9%

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

      1. +-commutative 70.9%

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

      2. associate-/l* 85.5%

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

      3. fma-define 85.5%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in a around inf 32.4%

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

   if -9.1999999999999997e-241 < t < 6.99999999999999968e-7

   1. Initial program 86.8%

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

      1. +-commutative 86.8%

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

      2. associate-/l* 94.7%

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

      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. Taylor expanded in y around 0 85.9%

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

      1. +-commutative 85.9%

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

      2. +-commutative 85.9%

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

      3. div-sub 85.9%

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

      4. mul-1-neg 85.9%

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

      5. associate-/l* 87.9%

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

      6. distribute-lft-neg-in 87.9%

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

      7. distribute-rgt-in 94.7%

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

      8. sub-neg 94.7%

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

      9. associate-*l/ 86.8%

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

      10. associate-*r/ 93.6%

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

      11. fma-define 93.5%

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

   7. Simplified 93.5%

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

   8. Taylor expanded in y around inf 45.3%

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

      1. div-sub 45.3%

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

   10. Simplified 45.3%

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

   11. Taylor expanded in t around 0 40.0%

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

   if 6.99999999999999968e-7 < t < 8.19999999999999959e99

   1. Initial program 77.1%

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

      1. +-commutative 77.1%

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

      2. associate-/l* 90.1%

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

      3. fma-define 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in y around 0 45.0%

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

      1. *-rgt-identity 45.0%

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

      2. mul-1-neg 45.0%

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

      3. associate-/l* 53.5%

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

      4. distribute-rgt-neg-in 53.5%

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

      5. mul-1-neg 53.5%

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

      6. distribute-lft-in 53.7%

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

      7. mul-1-neg 53.7%

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

      8. unsub-neg 53.7%

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

   7. Simplified 53.7%

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

   8. Taylor expanded in a around 0 41.0%

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

Alternative 10: 62.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-146}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-43}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.15e-146)
   (* y (/ (- z t) (- a t)))
   (if (<= t 2.9e-43)
     (+ x (* z (/ (- y x) a)))
     (if (<= t 8.5e+99) (/ z (/ (- a t) (- y x))) (+ y (* a (/ (- y x) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e-146) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 2.9e-43) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 8.5e+99) {
		tmp = z / ((a - t) / (y - x));
	} else {
		tmp = y + (a * ((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 <= (-1.15d-146)) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= 2.9d-43) then
        tmp = x + (z * ((y - x) / a))
    else if (t <= 8.5d+99) then
        tmp = z / ((a - t) / (y - x))
    else
        tmp = y + (a * ((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 <= -1.15e-146) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 2.9e-43) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 8.5e+99) {
		tmp = z / ((a - t) / (y - x));
	} else {
		tmp = y + (a * ((y - x) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.15e-146:
		tmp = y * ((z - t) / (a - t))
	elif t <= 2.9e-43:
		tmp = x + (z * ((y - x) / a))
	elif t <= 8.5e+99:
		tmp = z / ((a - t) / (y - x))
	else:
		tmp = y + (a * ((y - x) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.15e-146)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= 2.9e-43)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif (t <= 8.5e+99)
		tmp = Float64(z / Float64(Float64(a - t) / Float64(y - x)));
	else
		tmp = Float64(y + Float64(a * Float64(Float64(y - x) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.15e-146)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= 2.9e-43)
		tmp = x + (z * ((y - x) / a));
	elseif (t <= 8.5e+99)
		tmp = z / ((a - t) / (y - x));
	else
		tmp = y + (a * ((y - x) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.15e-146], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e-43], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+99], N[(z / N[(N[(a - t), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(a * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.15e-146

   1. Initial program 50.6%

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

      1. +-commutative 50.6%

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

      2. associate-/l* 76.8%

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

      3. fma-define 76.8%

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

   3. Simplified 76.8%

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

   5. Taylor expanded in y around 0 63.4%

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

      1. +-commutative 63.4%

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

      2. +-commutative 63.4%

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

      3. div-sub 63.4%

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

      4. mul-1-neg 63.4%

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

      5. associate-/l* 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 76.8%

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

      8. sub-neg 76.8%

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

      9. associate-*l/ 50.6%

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

      10. associate-*r/ 72.9%

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

      11. fma-define 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in y around inf 58.6%

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

      1. div-sub 58.6%

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

   10. Simplified 58.6%

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

   if -1.15e-146 < t < 2.9000000000000001e-43

   1. Initial program 88.9%

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

   3. Taylor expanded in t around 0 81.1%

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

      1. associate-/l* 85.7%

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

   5. Simplified 85.7%

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

   if 2.9000000000000001e-43 < t < 8.49999999999999984e99

   1. Initial program 82.1%

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

      1. +-commutative 82.1%

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

      2. associate-/l* 89.3%

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

      3. fma-define 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in z around inf 70.9%

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

      1. sub-div 70.9%

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

      2. clear-num 71.0%

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

      3. un-div-inv 70.9%

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

   7. Applied egg-rr 70.9%

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

   if 8.49999999999999984e99 < t

   1. Initial program 38.6%

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

      1. +-commutative 38.6%

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

      2. associate-/l* 69.1%

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

      3. fma-define 69.1%

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

   3. Simplified 69.1%

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

   5. Taylor expanded in z around inf 53.6%

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

      1. +-commutative 53.6%

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

      2. mul-1-neg 53.6%

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

      3. unsub-neg 53.6%

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

   7. Simplified 53.6%

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

   8. Taylor expanded in t around inf 62.1%

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

   9. Taylor expanded in z around 0 62.3%

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

       1. associate-/l* 66.4%

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

   11. Simplified 66.4%

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

Alternative 11: 57.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+55}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -3.2e+144)
   (* x (- 1.0 (/ z a)))
   (if (<= x 1.7e-20)
     (* y (/ (- z t) (- a t)))
     (if (<= x 1.9e+55) (+ x (* y (/ (- z t) a))) (* x (/ (- z a) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.2e+144) {
		tmp = x * (1.0 - (z / a));
	} else if (x <= 1.7e-20) {
		tmp = y * ((z - t) / (a - t));
	} else if (x <= 1.9e+55) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = 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 (x <= (-3.2d+144)) then
        tmp = x * (1.0d0 - (z / a))
    else if (x <= 1.7d-20) then
        tmp = y * ((z - t) / (a - t))
    else if (x <= 1.9d+55) then
        tmp = x + (y * ((z - t) / a))
    else
        tmp = 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 (x <= -3.2e+144) {
		tmp = x * (1.0 - (z / a));
	} else if (x <= 1.7e-20) {
		tmp = y * ((z - t) / (a - t));
	} else if (x <= 1.9e+55) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = x * ((z - a) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -3.2e+144:
		tmp = x * (1.0 - (z / a))
	elif x <= 1.7e-20:
		tmp = y * ((z - t) / (a - t))
	elif x <= 1.9e+55:
		tmp = x + (y * ((z - t) / a))
	else:
		tmp = x * ((z - a) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -3.2e+144)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (x <= 1.7e-20)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (x <= 1.9e+55)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	else
		tmp = Float64(x * Float64(Float64(z - a) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -3.2e+144)
		tmp = x * (1.0 - (z / a));
	elseif (x <= 1.7e-20)
		tmp = y * ((z - t) / (a - t));
	elseif (x <= 1.9e+55)
		tmp = x + (y * ((z - t) / a));
	else
		tmp = x * ((z - a) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3.2e+144], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e-20], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e+55], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.2000000000000001e144

   1. Initial program 70.9%

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

      1. +-commutative 70.9%

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

      2. associate-/l* 90.8%

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

      3. fma-define 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in y around 0 63.6%

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

      1. *-rgt-identity 63.6%

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

      2. mul-1-neg 63.6%

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

      3. associate-/l* 77.5%

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

      4. distribute-rgt-neg-in 77.5%

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

      5. mul-1-neg 77.5%

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

      6. distribute-lft-in 77.6%

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

      7. mul-1-neg 77.6%

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

      8. unsub-neg 77.6%

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

   7. Simplified 77.6%

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

   8. Taylor expanded in t around 0 61.1%

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

   if -3.2000000000000001e144 < x < 1.6999999999999999e-20

   1. Initial program 72.5%

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

      1. +-commutative 72.5%

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

      2. associate-/l* 90.4%

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

      3. fma-define 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in y around 0 83.4%

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

      1. +-commutative 83.4%

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

      2. +-commutative 83.4%

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

      3. div-sub 83.4%

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

      4. mul-1-neg 83.4%

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

      5. associate-/l* 87.8%

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

      6. distribute-lft-neg-in 87.8%

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

      7. distribute-rgt-in 90.4%

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

      8. sub-neg 90.4%

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

      9. associate-*l/ 72.5%

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

      10. associate-*r/ 88.3%

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

      11. fma-define 88.3%

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

   7. Simplified 88.3%

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

   8. Taylor expanded in y around inf 69.9%

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

      1. div-sub 69.9%

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

   10. Simplified 69.9%

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

   if 1.6999999999999999e-20 < x < 1.9e55

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 75.6%

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

      1. associate-/l* 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in y around inf 73.5%

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

   if 1.9e55 < x

   1. Initial program 37.2%

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

      1. +-commutative 37.2%

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

      2. associate-/l* 59.5%

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

      3. fma-define 59.5%

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

   3. Simplified 59.5%

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

   5. Taylor expanded in y around 0 33.7%

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

      1. *-rgt-identity 33.7%

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

      2. mul-1-neg 33.7%

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

      3. associate-/l* 47.7%

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

      4. distribute-rgt-neg-in 47.7%

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

      5. mul-1-neg 47.7%

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

      6. distribute-lft-in 47.7%

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

      7. mul-1-neg 47.7%

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

      8. unsub-neg 47.7%

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

   7. Simplified 47.7%

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

   8. Taylor expanded in t around inf 53.5%

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

      1. associate-*r/ 53.5%

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

      2. mul-1-neg 53.5%

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

      3. sub-neg 53.5%

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

      4. mul-1-neg 53.5%

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

   10. Simplified 53.5%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+55}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+95}:\\ \;\;\;\;y - \frac{\left(a - z\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+196}:\\ \;\;\;\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.9e+95)
   (- y (/ (* (- a z) (- x y)) t))
   (if (<= t 8e+196)
     (+ x (/ (* (- x y) (- t z)) (- a t)))
     (+ y (* a (/ (- y x) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.9e+95) {
		tmp = y - (((a - z) * (x - y)) / t);
	} else if (t <= 8e+196) {
		tmp = x + (((x - y) * (t - z)) / (a - t));
	} else {
		tmp = y + (a * ((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 <= (-1.9d+95)) then
        tmp = y - (((a - z) * (x - y)) / t)
    else if (t <= 8d+196) then
        tmp = x + (((x - y) * (t - z)) / (a - t))
    else
        tmp = y + (a * ((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 <= -1.9e+95) {
		tmp = y - (((a - z) * (x - y)) / t);
	} else if (t <= 8e+196) {
		tmp = x + (((x - y) * (t - z)) / (a - t));
	} else {
		tmp = y + (a * ((y - x) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.9e+95:
		tmp = y - (((a - z) * (x - y)) / t)
	elif t <= 8e+196:
		tmp = x + (((x - y) * (t - z)) / (a - t))
	else:
		tmp = y + (a * ((y - x) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.9e+95)
		tmp = Float64(y - Float64(Float64(Float64(a - z) * Float64(x - y)) / t));
	elseif (t <= 8e+196)
		tmp = Float64(x + Float64(Float64(Float64(x - y) * Float64(t - z)) / Float64(a - t)));
	else
		tmp = Float64(y + Float64(a * Float64(Float64(y - x) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.9e+95)
		tmp = y - (((a - z) * (x - y)) / t);
	elseif (t <= 8e+196)
		tmp = x + (((x - y) * (t - z)) / (a - t));
	else
		tmp = y + (a * ((y - x) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.9e+95], N[(y - N[(N[(N[(a - z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+196], N[(x + N[(N[(N[(x - y), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(a * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9e95

   1. Initial program 24.5%

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

      1. +-commutative 24.5%

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

      2. associate-/l* 63.2%

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

      3. fma-define 63.2%

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

   3. Simplified 63.2%

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

   5. Taylor expanded in t around inf 70.3%

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

      1. associate--l+ 70.3%

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

      2. associate-*r/ 70.3%

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

      3. associate-*r/ 70.3%

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

      4. mul-1-neg 70.3%

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

      5. div-sub 70.3%

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

      6. mul-1-neg 70.3%

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

      7. distribute-lft-out-- 70.3%

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

      8. associate-*r/ 70.3%

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

      9. mul-1-neg 70.3%

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

      10. unsub-neg 70.3%

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

      11. distribute-rgt-out-- 70.6%

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

   7. Simplified 70.6%

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

   if -1.9e95 < t < 7.9999999999999996e196

   1. Initial program 82.8%

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

   if 7.9999999999999996e196 < t

   1. Initial program 20.1%

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

      1. +-commutative 20.1%

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

      2. associate-/l* 62.7%

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

      3. fma-define 62.7%

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

   3. Simplified 62.7%

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

   5. Taylor expanded in z around inf 38.4%

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

      1. +-commutative 38.4%

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

      2. mul-1-neg 38.4%

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

      3. unsub-neg 38.4%

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

   7. Simplified 38.4%

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

   8. Taylor expanded in t around inf 61.2%

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

   9. Taylor expanded in z around 0 69.7%

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

       1. associate-/l* 75.9%

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

   11. Simplified 75.9%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+95}:\\ \;\;\;\;y - \frac{\left(a - z\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+196}:\\ \;\;\;\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot \frac{y - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 71.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{+95} \lor \neg \left(t \leq 8 \cdot 10^{+99}\right):\\ \;\;\;\;y + a \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{x - y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.45e+95) (not (<= t 8e+99)))
   (+ y (* a (/ (- y x) t)))
   (+ x (* z (/ (- x y) (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.45e+95) || !(t <= 8e+99)) {
		tmp = y + (a * ((y - x) / t));
	} else {
		tmp = x + (z * ((x - y) / (t - 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 <= (-2.45d+95)) .or. (.not. (t <= 8d+99))) then
        tmp = y + (a * ((y - x) / t))
    else
        tmp = x + (z * ((x - y) / (t - 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 <= -2.45e+95) || !(t <= 8e+99)) {
		tmp = y + (a * ((y - x) / t));
	} else {
		tmp = x + (z * ((x - y) / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.45e+95) or not (t <= 8e+99):
		tmp = y + (a * ((y - x) / t))
	else:
		tmp = x + (z * ((x - y) / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.45e+95) || !(t <= 8e+99))
		tmp = Float64(y + Float64(a * Float64(Float64(y - x) / t)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(x - y) / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.45e+95) || ~((t <= 8e+99)))
		tmp = y + (a * ((y - x) / t));
	else
		tmp = x + (z * ((x - y) / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.45e+95], N[Not[LessEqual[t, 8e+99]], $MachinePrecision]], N[(y + N[(a * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.4499999999999999e95 or 7.9999999999999997e99 < t

   1. Initial program 32.5%

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

      1. +-commutative 32.5%

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

      2. associate-/l* 66.5%

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

      3. fma-define 66.5%

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

   3. Simplified 66.5%

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

   5. Taylor expanded in z around inf 53.9%

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

      1. +-commutative 53.9%

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

      2. mul-1-neg 53.9%

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

      3. unsub-neg 53.9%

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

   7. Simplified 53.9%

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

   8. Taylor expanded in t around inf 58.2%

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

   9. Taylor expanded in z around 0 63.6%

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

       1. associate-/l* 66.9%

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

   11. Simplified 66.9%

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

   if -2.4499999999999999e95 < t < 7.9999999999999997e99

   1. Initial program 84.3%

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

   3. Taylor expanded in z around inf 72.4%

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

      1. associate-/l* 81.2%

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

   5. Simplified 81.2%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{+95} \lor \neg \left(t \leq 8 \cdot 10^{+99}\right):\\ \;\;\;\;y + a \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{x - y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 34.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+185}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-145}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.7e+185)
   y
   (if (<= t 2.15e-145) x (if (<= t 8.2e+99) (* x (/ z t)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.7e+185) {
		tmp = y;
	} else if (t <= 2.15e-145) {
		tmp = x;
	} else if (t <= 8.2e+99) {
		tmp = x * (z / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.7d+185)) then
        tmp = y
    else if (t <= 2.15d-145) then
        tmp = x
    else if (t <= 8.2d+99) then
        tmp = x * (z / t)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.7e+185) {
		tmp = y;
	} else if (t <= 2.15e-145) {
		tmp = x;
	} else if (t <= 8.2e+99) {
		tmp = x * (z / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.7e+185:
		tmp = y
	elif t <= 2.15e-145:
		tmp = x
	elif t <= 8.2e+99:
		tmp = x * (z / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.7e+185)
		tmp = y;
	elseif (t <= 2.15e-145)
		tmp = x;
	elseif (t <= 8.2e+99)
		tmp = Float64(x * Float64(z / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.7e+185)
		tmp = y;
	elseif (t <= 2.15e-145)
		tmp = x;
	elseif (t <= 8.2e+99)
		tmp = x * (z / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.7e+185], y, If[LessEqual[t, 2.15e-145], x, If[LessEqual[t, 8.2e+99], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.70000000000000009e185 or 8.19999999999999959e99 < t

   1. Initial program 34.3%

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

      1. +-commutative 34.3%

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

      2. associate-/l* 68.4%

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

      3. fma-define 68.4%

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

   3. Simplified 68.4%

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

   5. Taylor expanded in y around 0 52.6%

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

      1. +-commutative 52.6%

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

      2. +-commutative 52.6%

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

      3. div-sub 52.6%

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

      4. mul-1-neg 52.6%

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

      5. associate-/l* 68.4%

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

      6. distribute-lft-neg-in 68.4%

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

      7. distribute-rgt-in 68.4%

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

      8. sub-neg 68.4%

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

      9. associate-*l/ 34.3%

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

      10. associate-*r/ 63.9%

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

      11. fma-define 64.0%

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

   7. Simplified 64.0%

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

   8. Taylor expanded in t around inf 62.3%

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

   if -1.70000000000000009e185 < t < 2.15e-145

   1. Initial program 78.3%

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

      1. +-commutative 78.3%

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

      2. associate-/l* 90.6%

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

      3. fma-define 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in a around inf 31.4%

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

   if 2.15e-145 < t < 8.19999999999999959e99

   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* 90.7%

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

      3. fma-define 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in y around 0 50.8%

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

      1. *-rgt-identity 50.8%

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

      2. mul-1-neg 50.8%

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

      3. associate-/l* 53.7%

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

      4. distribute-rgt-neg-in 53.7%

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

      5. mul-1-neg 53.7%

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

      6. distribute-lft-in 53.6%

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

      7. mul-1-neg 53.6%

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

      8. unsub-neg 53.6%

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

   7. Simplified 53.6%

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

   8. Taylor expanded in a around 0 30.2%

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

Alternative 15: 63.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-146} \lor \neg \left(t \leq 1.2 \cdot 10^{-32}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.15e-146) (not (<= t 1.2e-32)))
   (* y (/ (- z t) (- a t)))
   (+ x (* z (/ (- y x) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.15e-146) || !(t <= 1.2e-32)) {
		tmp = y * ((z - t) / (a - 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 <= (-1.15d-146)) .or. (.not. (t <= 1.2d-32))) then
        tmp = y * ((z - t) / (a - 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 <= -1.15e-146) || !(t <= 1.2e-32)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z * ((y - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.15e-146) or not (t <= 1.2e-32):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + (z * ((y - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.15e-146) || !(t <= 1.2e-32))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - 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 <= -1.15e-146) || ~((t <= 1.2e-32)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + (z * ((y - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.15e-146], N[Not[LessEqual[t, 1.2e-32]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - 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 < -1.15e-146 or 1.2000000000000001e-32 < t

   1. Initial program 52.4%

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

      1. +-commutative 52.4%

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

      2. associate-/l* 77.0%

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

      3. fma-define 77.1%

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

   3. Simplified 77.1%

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

   5. Taylor expanded in y around 0 64.4%

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

      1. +-commutative 64.4%

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

      2. +-commutative 64.4%

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

      3. div-sub 64.4%

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

      4. mul-1-neg 64.4%

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

      5. associate-/l* 77.0%

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

      6. distribute-lft-neg-in 77.0%

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

      7. distribute-rgt-in 77.0%

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

      8. sub-neg 77.0%

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

      9. associate-*l/ 52.4%

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

      10. associate-*r/ 73.9%

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

      11. fma-define 74.1%

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

   7. Simplified 74.1%

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

   8. Taylor expanded in y around inf 60.1%

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

      1. div-sub 60.1%

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

   10. Simplified 60.1%

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

   if -1.15e-146 < t < 1.2000000000000001e-32

   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 t around 0 80.2%

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

      1. associate-/l* 84.6%

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

   5. Simplified 84.6%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-146} \lor \neg \left(t \leq 1.2 \cdot 10^{-32}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 63.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-33}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.8e-147)
   (* y (/ (- z t) (- a t)))
   (if (<= t 9.2e-33) (+ x (* z (/ (- y x) a))) (/ y (/ (- a t) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.8e-147) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 9.2e-33) {
		tmp = x + (z * ((y - x) / a));
	} else {
		tmp = y / ((a - t) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-9.8d-147)) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= 9.2d-33) then
        tmp = x + (z * ((y - x) / a))
    else
        tmp = y / ((a - t) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.8e-147) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 9.2e-33) {
		tmp = x + (z * ((y - x) / a));
	} else {
		tmp = y / ((a - t) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.8e-147:
		tmp = y * ((z - t) / (a - t))
	elif t <= 9.2e-33:
		tmp = x + (z * ((y - x) / a))
	else:
		tmp = y / ((a - t) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.8e-147)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= 9.2e-33)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	else
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.8e-147)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= 9.2e-33)
		tmp = x + (z * ((y - x) / a));
	else
		tmp = y / ((a - t) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.8e-147], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e-33], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.8000000000000001e-147

   1. Initial program 50.6%

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

      1. +-commutative 50.6%

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

      2. associate-/l* 76.8%

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

      3. fma-define 76.8%

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

   3. Simplified 76.8%

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

   5. Taylor expanded in y around 0 63.4%

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

      1. +-commutative 63.4%

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

      2. +-commutative 63.4%

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

      3. div-sub 63.4%

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

      4. mul-1-neg 63.4%

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

      5. associate-/l* 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 76.8%

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

      8. sub-neg 76.8%

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

      9. associate-*l/ 50.6%

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

      10. associate-*r/ 72.9%

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

      11. fma-define 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in y around inf 58.6%

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

      1. div-sub 58.6%

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

   10. Simplified 58.6%

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

   if -9.8000000000000001e-147 < t < 9.19999999999999942e-33

   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 t around 0 80.2%

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

      1. associate-/l* 84.6%

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

   5. Simplified 84.6%

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

   if 9.19999999999999942e-33 < t

   1. Initial program 54.1%

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

      1. +-commutative 54.1%

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

      2. associate-/l* 77.3%

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

      3. fma-define 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in y around 0 65.4%

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

      1. +-commutative 65.4%

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

      2. +-commutative 65.4%

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

      3. div-sub 65.3%

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

      4. mul-1-neg 65.3%

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

      5. associate-/l* 77.3%

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

      6. distribute-lft-neg-in 77.3%

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

      7. distribute-rgt-in 77.3%

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

      8. sub-neg 77.3%

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

      9. associate-*l/ 54.1%

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

      10. associate-*r/ 74.8%

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

      11. fma-define 75.1%

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

   7. Simplified 75.1%

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

   8. Taylor expanded in y around inf 61.5%

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

      1. div-sub 61.5%

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

   10. Simplified 61.5%

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

       1. clear-num 61.5%

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

       2. un-div-inv 61.5%

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

   12. Applied egg-rr 61.5%

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

Alternative 17: 57.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+26}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.4e+144)
   (* x (- 1.0 (/ z a)))
   (if (<= x 1.9e+26) (* y (/ (- z t) (- a t))) (* x (/ (- z a) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.4e+144) {
		tmp = x * (1.0 - (z / a));
	} else if (x <= 1.9e+26) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = 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 (x <= (-2.4d+144)) then
        tmp = x * (1.0d0 - (z / a))
    else if (x <= 1.9d+26) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = 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 (x <= -2.4e+144) {
		tmp = x * (1.0 - (z / a));
	} else if (x <= 1.9e+26) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x * ((z - a) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.4e+144:
		tmp = x * (1.0 - (z / a))
	elif x <= 1.9e+26:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x * ((z - a) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.4e+144)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (x <= 1.9e+26)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x * Float64(Float64(z - a) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.4e+144)
		tmp = x * (1.0 - (z / a));
	elseif (x <= 1.9e+26)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x * ((z - a) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.4e+144], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e+26], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.4000000000000001e144

   1. Initial program 70.9%

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

      1. +-commutative 70.9%

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

      2. associate-/l* 90.8%

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

      3. fma-define 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in y around 0 63.6%

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

      1. *-rgt-identity 63.6%

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

      2. mul-1-neg 63.6%

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

      3. associate-/l* 77.5%

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

      4. distribute-rgt-neg-in 77.5%

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

      5. mul-1-neg 77.5%

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

      6. distribute-lft-in 77.6%

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

      7. mul-1-neg 77.6%

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

      8. unsub-neg 77.6%

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

   7. Simplified 77.6%

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

   8. Taylor expanded in t around 0 61.1%

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

   if -2.4000000000000001e144 < x < 1.9000000000000001e26

   1. Initial program 74.6%

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

      1. +-commutative 74.6%

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

      2. associate-/l* 91.1%

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

      3. fma-define 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in y around 0 84.7%

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

      1. +-commutative 84.7%

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

      2. +-commutative 84.7%

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

      3. div-sub 84.7%

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

      4. mul-1-neg 84.7%

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

      5. associate-/l* 88.7%

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

      6. distribute-lft-neg-in 88.7%

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

      7. distribute-rgt-in 91.1%

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

      8. sub-neg 91.1%

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

      9. associate-*l/ 74.6%

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

      10. associate-*r/ 88.7%

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

      11. fma-define 88.6%

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

   7. Simplified 88.6%

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

   8. Taylor expanded in y around inf 68.2%

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

      1. div-sub 68.2%

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

   10. Simplified 68.2%

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

   if 1.9000000000000001e26 < x

   1. Initial program 40.3%

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

      1. +-commutative 40.3%

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

      2. associate-/l* 61.5%

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

      3. fma-define 61.5%

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

   3. Simplified 61.5%

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

   5. Taylor expanded in y around 0 36.9%

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

      1. *-rgt-identity 36.9%

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

      2. mul-1-neg 36.9%

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

      3. associate-/l* 50.2%

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

      4. distribute-rgt-neg-in 50.2%

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

      5. mul-1-neg 50.2%

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

      6. distribute-lft-in 50.3%

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

      7. mul-1-neg 50.3%

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

      8. unsub-neg 50.3%

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

   7. Simplified 50.3%

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

   8. Taylor expanded in t around inf 52.6%

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

      1. associate-*r/ 52.6%

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

      2. mul-1-neg 52.6%

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

      3. sub-neg 52.6%

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

      4. mul-1-neg 52.6%

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

   10. Simplified 52.6%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+26}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 47.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+187}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.1e+187) y (if (<= t 8.5e+71) (* x (- 1.0 (/ z a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.1e+187) {
		tmp = y;
	} else if (t <= 8.5e+71) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.1d+187)) then
        tmp = y
    else if (t <= 8.5d+71) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.1e+187) {
		tmp = y;
	} else if (t <= 8.5e+71) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.1e+187:
		tmp = y
	elif t <= 8.5e+71:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.1e+187)
		tmp = y;
	elseif (t <= 8.5e+71)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.1e+187)
		tmp = y;
	elseif (t <= 8.5e+71)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.1e+187], y, If[LessEqual[t, 8.5e+71], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -3.10000000000000012e187 or 8.4999999999999996e71 < t

   1. Initial program 37.6%

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

      1. +-commutative 37.6%

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

      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 y around 0 55.0%

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

      1. +-commutative 55.0%

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

      2. +-commutative 55.0%

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

      3. div-sub 55.0%

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

      4. mul-1-neg 55.0%

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

      5. associate-/l* 68.8%

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

      6. distribute-lft-neg-in 68.8%

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

      7. distribute-rgt-in 68.8%

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

      8. sub-neg 68.8%

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

      9. associate-*l/ 37.6%

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

      10. associate-*r/ 64.5%

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

      11. fma-define 64.7%

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

   7. Simplified 64.7%

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

   8. Taylor expanded in t around inf 60.6%

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

   if -3.10000000000000012e187 < t < 8.4999999999999996e71

   1. Initial program 79.0%

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

      1. +-commutative 79.0%

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

      2. associate-/l* 90.9%

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

      3. fma-define 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in y around 0 47.1%

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

      1. *-rgt-identity 47.1%

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

      2. mul-1-neg 47.1%

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

      3. associate-/l* 53.7%

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

      4. distribute-rgt-neg-in 53.7%

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

      5. mul-1-neg 53.7%

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

      6. distribute-lft-in 53.7%

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

      7. mul-1-neg 53.7%

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

      8. unsub-neg 53.7%

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

   7. Simplified 53.7%

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

   8. Taylor expanded in t around 0 46.3%

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

Alternative 19: 36.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+185}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.7e+185) y (if (<= t 2.2e+47) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.7e+185) {
		tmp = y;
	} else if (t <= 2.2e+47) {
		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 <= (-1.7d+185)) then
        tmp = y
    else if (t <= 2.2d+47) 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 <= -1.7e+185) {
		tmp = y;
	} else if (t <= 2.2e+47) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.7e+185:
		tmp = y
	elif t <= 2.2e+47:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.7e+185)
		tmp = y;
	elseif (t <= 2.2e+47)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.7e+185)
		tmp = y;
	elseif (t <= 2.2e+47)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.7e+185], y, If[LessEqual[t, 2.2e+47], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -1.70000000000000009e185 or 2.1999999999999999e47 < t

   1. Initial program 37.6%

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

      1. +-commutative 37.6%

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

      2. associate-/l* 69.9%

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

      3. fma-define 69.9%

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

   3. Simplified 69.9%

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

   5. Taylor expanded in y around 0 54.4%

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

      1. +-commutative 54.4%

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

      2. +-commutative 54.4%

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

      3. div-sub 54.4%

         \[\leadsto \left(y \cdot \color{blue}{\frac{z - t}{a - t}} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x \]

      4. mul-1-neg 54.4%

         \[\leadsto \left(y \cdot \frac{z - t}{a - t} + \color{blue}{\left(-\frac{x \cdot \left(z - t\right)}{a - t}\right)}\right) + x \]

      5. associate-/l* 69.9%

         \[\leadsto \left(y \cdot \frac{z - t}{a - t} + \left(-\color{blue}{x \cdot \frac{z - t}{a - t}}\right)\right) + x \]

      6. distribute-lft-neg-in 69.9%

         \[\leadsto \left(y \cdot \frac{z - t}{a - t} + \color{blue}{\left(-x\right) \cdot \frac{z - t}{a - t}}\right) + x \]

      7. distribute-rgt-in 69.9%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y + \left(-x\right)\right)} + x \]

      8. sub-neg 69.9%

         \[\leadsto \frac{z - t}{a - t} \cdot \color{blue}{\left(y - x\right)} + x \]

      9. associate-*l/ 37.6%

         \[\leadsto \color{blue}{\frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t}} + x \]

      10. associate-*r/ 65.7%

          \[\leadsto \color{blue}{\left(z - t\right) \cdot \frac{y - x}{a - t}} + x \]

      11. fma-define 65.9%

          \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   7. Simplified 65.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   8. Taylor expanded in t around inf 58.6%

      \[\leadsto \color{blue}{y} \]

   if -1.70000000000000009e185 < t < 2.1999999999999999e47

   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* 90.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. fma-define 90.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   3. Simplified 90.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 26.4%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 25.3% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x;
}

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 66.1%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Step-by-step derivation

   1. +-commutative 66.1%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

   2. associate-/l* 84.0%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

   3. fma-define 84.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

3. Simplified 84.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
4. Add Preprocessing

5. Taylor expanded in a around inf 19.6%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Alternative 21: 2.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 66.1%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Step-by-step derivation

   1. +-commutative 66.1%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

   2. associate-/l* 84.0%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

   3. fma-define 84.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

3. Simplified 84.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 36.1%

   \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} \]
6. Step-by-step derivation

   1. *-rgt-identity 36.1%

      \[\leadsto \color{blue}{x \cdot 1} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} \]

   2. mul-1-neg 36.1%

      \[\leadsto x \cdot 1 + \color{blue}{\left(-\frac{x \cdot \left(z - t\right)}{a - t}\right)} \]

   3. associate-/l* 41.7%

      \[\leadsto x \cdot 1 + \left(-\color{blue}{x \cdot \frac{z - t}{a - t}}\right) \]

   4. distribute-rgt-neg-in 41.7%

      \[\leadsto x \cdot 1 + \color{blue}{x \cdot \left(-\frac{z - t}{a - t}\right)} \]

   5. mul-1-neg 41.7%

      \[\leadsto x \cdot 1 + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t}\right)} \]

   6. distribute-lft-in 41.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

   7. mul-1-neg 41.7%

      \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z - t}{a - t}\right)}\right) \]

   8. unsub-neg 41.7%

      \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z - t}{a - t}\right)} \]

7. Simplified 41.7%

   \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z - t}{a - t}\right)} \]

8. Taylor expanded in t around inf 2.6%

   \[\leadsto x \cdot \left(1 - \color{blue}{1}\right) \]

9. Taylor expanded in x around 0 2.6%

   \[\leadsto \color{blue}{0} \]
10. Add Preprocessing

Developer Target 1: 86.5% 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 2024139 
(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))))