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

Percentage Accurate: 68.6% → 91.0%

Time: 15.5s

Alternatives: 20

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-279}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+289}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z)))))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-279)
       t_2
       (if (<= t_2 0.0)
         (+ t (/ (* (- t x) (- a y)) z))
         (if (<= t_2 5e+289) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-279) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 5e+289) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-279) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 5e+289) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	t_2 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-279:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t + (((t - x) * (a - y)) / z)
	elif t_2 <= 5e+289:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-279)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (t_2 <= 5e+289)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	t_2 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-279)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (t_2 <= 5e+289)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-279], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+289], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -inf.0 or 5.00000000000000031e289 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 36.6%

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

      1. associate-/l* 85.8%

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

   3. Simplified 85.8%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -2.00000000000000011e-279 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 5.00000000000000031e289

   1. Initial program 98.3%

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

   if -2.00000000000000011e-279 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.2%

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

      1. associate-/l* 4.0%

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

   3. Simplified 4.0%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. div-sub 99.8%

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

      6. mul-1-neg 99.8%

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

      7. distribute-lft-out-- 99.8%

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

      8. associate-*r/ 99.8%

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

      9. mul-1-neg 99.8%

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

      10. unsub-neg 99.8%

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

      11. distribute-rgt-out-- 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -\infty:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -2 \cdot 10^{-279}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 5 \cdot 10^{+289}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ t_2 := \frac{t - x}{z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-279} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(a \cdot t\_2 - \left(y \cdot t\_2 - a \cdot \frac{\left(t - x\right) \cdot \left(a - y\right)}{{z}^{2}}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))) (t_2 (/ (- t x) z)))
   (if (or (<= t_1 -2e-279) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+
      t
      (- (* a t_2) (- (* y t_2) (* a (/ (* (- t x) (- a y)) (pow z 2.0)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double t_2 = (t - x) / z;
	double tmp;
	if ((t_1 <= -2e-279) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + ((a * t_2) - ((y * t_2) - (a * (((t - x) * (a - y)) / pow(z, 2.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (((y - z) * (t - x)) / (a - z))
    t_2 = (t - x) / z
    if ((t_1 <= (-2d-279)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t + ((a * t_2) - ((y * t_2) - (a * (((t - x) * (a - y)) / (z ** 2.0d0)))))
    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 - z) * (t - x)) / (a - z));
	double t_2 = (t - x) / z;
	double tmp;
	if ((t_1 <= -2e-279) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + ((a * t_2) - ((y * t_2) - (a * (((t - x) * (a - y)) / Math.pow(z, 2.0)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * (t - x)) / (a - z))
	t_2 = (t - x) / z
	tmp = 0
	if (t_1 <= -2e-279) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t + ((a * t_2) - ((y * t_2) - (a * (((t - x) * (a - y)) / math.pow(z, 2.0)))))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	t_2 = Float64(Float64(t - x) / z)
	tmp = 0.0
	if ((t_1 <= -2e-279) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(a * t_2) - Float64(Float64(y * t_2) - Float64(a * Float64(Float64(Float64(t - x) * Float64(a - y)) / (z ^ 2.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) * (t - x)) / (a - z));
	t_2 = (t - x) / z;
	tmp = 0.0;
	if ((t_1 <= -2e-279) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t + ((a * t_2) - ((y * t_2) - (a * (((t - x) * (a - y)) / (z ^ 2.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-279], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(a * t$95$2), $MachinePrecision] - N[(N[(y * t$95$2), $MachinePrecision] - N[(a * N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -2.00000000000000011e-279 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 73.1%

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

      1. associate-/l* 86.4%

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

   3. Simplified 86.4%

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

      1. *-commutative 86.4%

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

      2. associate-*l/ 73.1%

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

      3. associate-*r/ 92.3%

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

      4. clear-num 92.3%

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

      5. un-div-inv 92.8%

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

   6. Applied egg-rr 92.8%

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

   if -2.00000000000000011e-279 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.2%

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

      1. associate-/l* 4.0%

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

   3. Simplified 4.0%

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

      1. *-commutative 4.0%

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

      2. associate-*l/ 4.2%

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

      3. associate-*r/ 4.2%

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

      4. clear-num 4.2%

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

      5. un-div-inv 4.2%

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

   6. Applied egg-rr 4.2%

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

   7. Taylor expanded in z around inf 99.8%

      \[\leadsto \color{blue}{\left(t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}}\right)\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   8. Step-by-step derivation

      1. associate--l+ 99.8%

         \[\leadsto \color{blue}{t + \left(\left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. sub-neg 99.8%

         \[\leadsto t + \color{blue}{\left(\left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}}\right) + \left(--1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)\right)} \]

   9. Simplified 100.0%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -2 \cdot 10^{-279} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(a \cdot \frac{t - x}{z} - \left(y \cdot \frac{t - x}{z} - a \cdot \frac{\left(t - x\right) \cdot \left(a - y\right)}{{z}^{2}}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-279} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -2e-279) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ t (/ (* (- t x) (- a y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -2e-279) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	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 - z) * (t - x)) / (a - z))
    if ((t_1 <= (-2d-279)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t + (((t - x) * (a - y)) / z)
    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 - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -2e-279) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if (t_1 <= -2e-279) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -2e-279) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -2e-279) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-279], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -2.00000000000000011e-279 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 73.1%

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

      1. associate-/l* 86.4%

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

   3. Simplified 86.4%

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

      1. *-commutative 86.4%

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

      2. associate-*l/ 73.1%

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

      3. associate-*r/ 92.3%

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

      4. clear-num 92.3%

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

      5. un-div-inv 92.8%

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

   6. Applied egg-rr 92.8%

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

   if -2.00000000000000011e-279 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.2%

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

      1. associate-/l* 4.0%

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

   3. Simplified 4.0%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. div-sub 99.8%

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

      6. mul-1-neg 99.8%

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

      7. distribute-lft-out-- 99.8%

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

      8. associate-*r/ 99.8%

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

      9. mul-1-neg 99.8%

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

      10. unsub-neg 99.8%

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

      11. distribute-rgt-out-- 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -2 \cdot 10^{-279} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{+30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-151}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-224}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-176}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1050:\\ \;\;\;\;t + \left(x - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (* (- y z) (/ (- t x) a)))))
   (if (<= a -4.8e+30)
     t_2
     (if (<= a -5.8e-124)
       t_1
       (if (<= a -7.5e-151)
         (* x (+ (/ (- y z) (- z a)) 1.0))
         (if (<= a -9.2e-224)
           t_1
           (if (<= a 4.7e-176)
             (+ t (/ (* y (- x t)) z))
             (if (<= a 1050.0) (+ t (* (- x t) (/ y z))) t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + ((y - z) * ((t - x) / a));
	double tmp;
	if (a <= -4.8e+30) {
		tmp = t_2;
	} else if (a <= -5.8e-124) {
		tmp = t_1;
	} else if (a <= -7.5e-151) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else if (a <= -9.2e-224) {
		tmp = t_1;
	} else if (a <= 4.7e-176) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 1050.0) {
		tmp = t + ((x - t) * (y / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + ((y - z) * ((t - x) / a))
    if (a <= (-4.8d+30)) then
        tmp = t_2
    else if (a <= (-5.8d-124)) then
        tmp = t_1
    else if (a <= (-7.5d-151)) then
        tmp = x * (((y - z) / (z - a)) + 1.0d0)
    else if (a <= (-9.2d-224)) then
        tmp = t_1
    else if (a <= 4.7d-176) then
        tmp = t + ((y * (x - t)) / z)
    else if (a <= 1050.0d0) then
        tmp = t + ((x - t) * (y / z))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + ((y - z) * ((t - x) / a));
	double tmp;
	if (a <= -4.8e+30) {
		tmp = t_2;
	} else if (a <= -5.8e-124) {
		tmp = t_1;
	} else if (a <= -7.5e-151) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else if (a <= -9.2e-224) {
		tmp = t_1;
	} else if (a <= 4.7e-176) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 1050.0) {
		tmp = t + ((x - t) * (y / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + ((y - z) * ((t - x) / a))
	tmp = 0
	if a <= -4.8e+30:
		tmp = t_2
	elif a <= -5.8e-124:
		tmp = t_1
	elif a <= -7.5e-151:
		tmp = x * (((y - z) / (z - a)) + 1.0)
	elif a <= -9.2e-224:
		tmp = t_1
	elif a <= 4.7e-176:
		tmp = t + ((y * (x - t)) / z)
	elif a <= 1050.0:
		tmp = t + ((x - t) * (y / z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -4.8e+30)
		tmp = t_2;
	elseif (a <= -5.8e-124)
		tmp = t_1;
	elseif (a <= -7.5e-151)
		tmp = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0));
	elseif (a <= -9.2e-224)
		tmp = t_1;
	elseif (a <= 4.7e-176)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	elseif (a <= 1050.0)
		tmp = Float64(t + Float64(Float64(x - t) * Float64(y / z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + ((y - z) * ((t - x) / a));
	tmp = 0.0;
	if (a <= -4.8e+30)
		tmp = t_2;
	elseif (a <= -5.8e-124)
		tmp = t_1;
	elseif (a <= -7.5e-151)
		tmp = x * (((y - z) / (z - a)) + 1.0);
	elseif (a <= -9.2e-224)
		tmp = t_1;
	elseif (a <= 4.7e-176)
		tmp = t + ((y * (x - t)) / z);
	elseif (a <= 1050.0)
		tmp = t + ((x - t) * (y / z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.8e+30], t$95$2, If[LessEqual[a, -5.8e-124], t$95$1, If[LessEqual[a, -7.5e-151], N[(x * N[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.2e-224], t$95$1, If[LessEqual[a, 4.7e-176], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1050.0], N[(t + N[(N[(x - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.7999999999999999e30 or 1050 < a

   1. Initial program 66.9%

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

      1. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in a around inf 78.6%

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

   if -4.7999999999999999e30 < a < -5.8000000000000004e-124 or -7.5000000000000004e-151 < a < -9.1999999999999995e-224

   1. Initial program 73.7%

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

      1. associate-/l* 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in x around 0 66.5%

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

      1. associate-/l* 76.3%

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

   7. Simplified 76.3%

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

   if -5.8000000000000004e-124 < a < -7.5000000000000004e-151

   1. Initial program 70.5%

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

      1. associate-/l* 77.8%

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

   3. Simplified 77.8%

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

   5. Taylor expanded in x around inf 70.5%

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

      1. mul-1-neg 70.5%

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

      2. unsub-neg 70.5%

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

   7. Simplified 70.5%

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

   if -9.1999999999999995e-224 < a < 4.69999999999999984e-176

   1. Initial program 67.1%

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

      1. associate-/l* 67.2%

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

   3. Simplified 67.2%

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

   5. Taylor expanded in a around 0 66.7%

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

      1. associate-*r/ 66.7%

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

      2. associate-*r* 66.7%

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

      3. neg-mul-1 66.7%

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

      4. *-commutative 66.7%

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

   7. Simplified 66.7%

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

   8. Taylor expanded in y around 0 67.2%

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

      1. +-commutative 67.2%

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

      2. div-sub 67.3%

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

      3. associate-/l* 72.6%

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

      4. mul-1-neg 72.6%

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

      5. unsub-neg 72.6%

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

      6. associate-/l* 67.3%

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

   10. Simplified 67.3%

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

   11. Taylor expanded in z around inf 99.5%

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

   if 4.69999999999999984e-176 < a < 1050

   1. Initial program 64.6%

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

      1. associate-/l* 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in a around 0 48.9%

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

      1. associate-*r/ 48.9%

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

      2. associate-*r* 48.9%

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

      3. neg-mul-1 48.9%

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

      4. *-commutative 48.9%

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

   7. Simplified 48.9%

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

   8. Taylor expanded in y around 0 60.8%

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

      1. +-commutative 60.8%

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

      2. div-sub 63.0%

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

      3. associate-/l* 59.1%

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

      4. mul-1-neg 59.1%

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

      5. unsub-neg 59.1%

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

      6. associate-/l* 63.0%

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

   10. Simplified 63.0%

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

   11. Taylor expanded in y around 0 71.9%

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

       1. div-sub 74.0%

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

   13. Simplified 74.0%

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

       1. clear-num 73.9%

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

       2. un-div-inv 73.9%

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

   15. Applied egg-rr 73.9%

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

       1. associate-/r/ 77.9%

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

   17. Simplified 77.9%

       \[\leadsto t + \color{blue}{\frac{y}{z} \cdot \left(x - t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+30}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-124}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-151}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-224}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-176}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1050:\\ \;\;\;\;t + \left(x - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -7 \cdot 10^{+26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-150}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-40}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;a \leq 150:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (* (- y z) (/ (- t x) a)))))
   (if (<= a -7e+26)
     t_2
     (if (<= a -5.8e-124)
       t_1
       (if (<= a -8.5e-150)
         (* x (+ (/ (- y z) (- z a)) 1.0))
         (if (<= a -2.25e-226)
           t_1
           (if (<= a 2.6e-40)
             (+ t (/ (* (- t x) (- a y)) z))
             (if (<= a 150.0) (- t (* y (/ (- t x) z))) t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + ((y - z) * ((t - x) / a));
	double tmp;
	if (a <= -7e+26) {
		tmp = t_2;
	} else if (a <= -5.8e-124) {
		tmp = t_1;
	} else if (a <= -8.5e-150) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else if (a <= -2.25e-226) {
		tmp = t_1;
	} else if (a <= 2.6e-40) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (a <= 150.0) {
		tmp = t - (y * ((t - x) / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + ((y - z) * ((t - x) / a))
    if (a <= (-7d+26)) then
        tmp = t_2
    else if (a <= (-5.8d-124)) then
        tmp = t_1
    else if (a <= (-8.5d-150)) then
        tmp = x * (((y - z) / (z - a)) + 1.0d0)
    else if (a <= (-2.25d-226)) then
        tmp = t_1
    else if (a <= 2.6d-40) then
        tmp = t + (((t - x) * (a - y)) / z)
    else if (a <= 150.0d0) then
        tmp = t - (y * ((t - x) / z))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + ((y - z) * ((t - x) / a));
	double tmp;
	if (a <= -7e+26) {
		tmp = t_2;
	} else if (a <= -5.8e-124) {
		tmp = t_1;
	} else if (a <= -8.5e-150) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else if (a <= -2.25e-226) {
		tmp = t_1;
	} else if (a <= 2.6e-40) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (a <= 150.0) {
		tmp = t - (y * ((t - x) / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + ((y - z) * ((t - x) / a))
	tmp = 0
	if a <= -7e+26:
		tmp = t_2
	elif a <= -5.8e-124:
		tmp = t_1
	elif a <= -8.5e-150:
		tmp = x * (((y - z) / (z - a)) + 1.0)
	elif a <= -2.25e-226:
		tmp = t_1
	elif a <= 2.6e-40:
		tmp = t + (((t - x) * (a - y)) / z)
	elif a <= 150.0:
		tmp = t - (y * ((t - x) / z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -7e+26)
		tmp = t_2;
	elseif (a <= -5.8e-124)
		tmp = t_1;
	elseif (a <= -8.5e-150)
		tmp = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0));
	elseif (a <= -2.25e-226)
		tmp = t_1;
	elseif (a <= 2.6e-40)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (a <= 150.0)
		tmp = Float64(t - Float64(y * Float64(Float64(t - x) / z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + ((y - z) * ((t - x) / a));
	tmp = 0.0;
	if (a <= -7e+26)
		tmp = t_2;
	elseif (a <= -5.8e-124)
		tmp = t_1;
	elseif (a <= -8.5e-150)
		tmp = x * (((y - z) / (z - a)) + 1.0);
	elseif (a <= -2.25e-226)
		tmp = t_1;
	elseif (a <= 2.6e-40)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (a <= 150.0)
		tmp = t - (y * ((t - x) / z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7e+26], t$95$2, If[LessEqual[a, -5.8e-124], t$95$1, If[LessEqual[a, -8.5e-150], N[(x * N[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.25e-226], t$95$1, If[LessEqual[a, 2.6e-40], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 150.0], N[(t - N[(y * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6.9999999999999998e26 or 150 < a

   1. Initial program 66.9%

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

      1. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in a around inf 78.6%

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

   if -6.9999999999999998e26 < a < -5.8000000000000004e-124 or -8.4999999999999997e-150 < a < -2.25000000000000006e-226

   1. Initial program 73.7%

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

      1. associate-/l* 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in x around 0 66.5%

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

      1. associate-/l* 76.3%

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

   7. Simplified 76.3%

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

   if -5.8000000000000004e-124 < a < -8.4999999999999997e-150

   1. Initial program 70.5%

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

      1. associate-/l* 77.8%

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

   3. Simplified 77.8%

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

   5. Taylor expanded in x around inf 70.5%

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

      1. mul-1-neg 70.5%

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

      2. unsub-neg 70.5%

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

   7. Simplified 70.5%

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

   if -2.25000000000000006e-226 < a < 2.6000000000000001e-40

   1. Initial program 69.3%

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

      1. associate-/l* 72.1%

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

   3. Simplified 72.1%

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

   5. Taylor expanded in z around inf 89.3%

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

      1. associate--l+ 89.3%

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

      2. associate-*r/ 89.3%

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

      3. associate-*r/ 89.3%

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

      4. mul-1-neg 89.3%

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

      5. div-sub 89.3%

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

      6. mul-1-neg 89.3%

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

      7. distribute-lft-out-- 89.3%

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

      8. associate-*r/ 89.3%

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

      9. mul-1-neg 89.3%

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

      10. unsub-neg 89.3%

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

      11. distribute-rgt-out-- 89.3%

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

   7. Simplified 89.3%

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

   if 2.6000000000000001e-40 < a < 150

   1. Initial program 45.5%

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

      1. associate-/l* 75.8%

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

   3. Simplified 75.8%

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

   5. Taylor expanded in a around 0 37.7%

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

      1. associate-*r/ 37.7%

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

      2. associate-*r* 37.7%

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

      3. neg-mul-1 37.7%

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

      4. *-commutative 37.7%

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

   7. Simplified 37.7%

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

   8. Taylor expanded in y around 0 75.8%

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

      1. +-commutative 75.8%

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

      2. div-sub 75.8%

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

      3. associate-/l* 53.2%

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

      4. mul-1-neg 53.2%

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

      5. unsub-neg 53.2%

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

      6. associate-/l* 75.8%

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

   10. Simplified 75.8%

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

   11. Taylor expanded in y around 0 84.3%

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

       1. div-sub 84.3%

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

   13. Simplified 84.3%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+26}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-124}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-150}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-226}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-40}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;a \leq 150:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(x - t\right)}{z}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -1.85 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-231}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-281}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-107}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+209}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- x t)) z)) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= a -1.85e+146)
     x
     (if (<= a -1e-231)
       t_2
       (if (<= a -1.25e-281)
         t_1
         (if (<= a 2.6e-107)
           t_2
           (if (<= a 1.25e-59) t_1 (if (<= a 1.2e+209) t_2 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (x - t)) / z;
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -1.85e+146) {
		tmp = x;
	} else if (a <= -1e-231) {
		tmp = t_2;
	} else if (a <= -1.25e-281) {
		tmp = t_1;
	} else if (a <= 2.6e-107) {
		tmp = t_2;
	} else if (a <= 1.25e-59) {
		tmp = t_1;
	} else if (a <= 1.2e+209) {
		tmp = t_2;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * (x - t)) / z
    t_2 = t * ((y - z) / (a - z))
    if (a <= (-1.85d+146)) then
        tmp = x
    else if (a <= (-1d-231)) then
        tmp = t_2
    else if (a <= (-1.25d-281)) then
        tmp = t_1
    else if (a <= 2.6d-107) then
        tmp = t_2
    else if (a <= 1.25d-59) then
        tmp = t_1
    else if (a <= 1.2d+209) then
        tmp = t_2
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (x - t)) / z;
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -1.85e+146) {
		tmp = x;
	} else if (a <= -1e-231) {
		tmp = t_2;
	} else if (a <= -1.25e-281) {
		tmp = t_1;
	} else if (a <= 2.6e-107) {
		tmp = t_2;
	} else if (a <= 1.25e-59) {
		tmp = t_1;
	} else if (a <= 1.2e+209) {
		tmp = t_2;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (x - t)) / z
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if a <= -1.85e+146:
		tmp = x
	elif a <= -1e-231:
		tmp = t_2
	elif a <= -1.25e-281:
		tmp = t_1
	elif a <= 2.6e-107:
		tmp = t_2
	elif a <= 1.25e-59:
		tmp = t_1
	elif a <= 1.2e+209:
		tmp = t_2
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(x - t)) / z)
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (a <= -1.85e+146)
		tmp = x;
	elseif (a <= -1e-231)
		tmp = t_2;
	elseif (a <= -1.25e-281)
		tmp = t_1;
	elseif (a <= 2.6e-107)
		tmp = t_2;
	elseif (a <= 1.25e-59)
		tmp = t_1;
	elseif (a <= 1.2e+209)
		tmp = t_2;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (x - t)) / z;
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (a <= -1.85e+146)
		tmp = x;
	elseif (a <= -1e-231)
		tmp = t_2;
	elseif (a <= -1.25e-281)
		tmp = t_1;
	elseif (a <= 2.6e-107)
		tmp = t_2;
	elseif (a <= 1.25e-59)
		tmp = t_1;
	elseif (a <= 1.2e+209)
		tmp = t_2;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.85e+146], x, If[LessEqual[a, -1e-231], t$95$2, If[LessEqual[a, -1.25e-281], t$95$1, If[LessEqual[a, 2.6e-107], t$95$2, If[LessEqual[a, 1.25e-59], t$95$1, If[LessEqual[a, 1.2e+209], t$95$2, x]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.85000000000000002e146 or 1.19999999999999998e209 < a

   1. Initial program 65.2%

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

      1. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in a around inf 60.3%

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

   if -1.85000000000000002e146 < a < -9.9999999999999999e-232 or -1.2499999999999999e-281 < a < 2.6000000000000001e-107 or 1.25e-59 < a < 1.19999999999999998e209

   1. Initial program 67.2%

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

      1. associate-/l* 75.9%

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

   3. Simplified 75.9%

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

   5. Taylor expanded in x around 0 46.2%

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

      1. associate-/l* 62.6%

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

   7. Simplified 62.6%

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

   if -9.9999999999999999e-232 < a < -1.2499999999999999e-281 or 2.6000000000000001e-107 < a < 1.25e-59

   1. Initial program 84.4%

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

      1. associate-/l* 79.1%

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

   3. Simplified 79.1%

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

   5. Taylor expanded in a around 0 79.4%

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

      1. associate-*r/ 79.4%

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

      2. associate-*r* 79.4%

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

      3. neg-mul-1 79.4%

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

      4. *-commutative 79.4%

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

   7. Simplified 79.4%

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

   8. Taylor expanded in y around -inf 84.2%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-231}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-281}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-107}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-59}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+209}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{-150}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-221}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-176}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 0.0115:\\ \;\;\;\;t + \left(x - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= a -9.5e+29)
     (+ x (/ (- y z) (/ a t)))
     (if (<= a -8.5e-120)
       t_1
       (if (<= a -9.6e-150)
         (* x (+ (/ (- y z) (- z a)) 1.0))
         (if (<= a -5e-221)
           t_1
           (if (<= a 4.7e-176)
             (+ t (/ (* y (- x t)) z))
             (if (<= a 0.0115)
               (+ t (* (- x t) (/ y z)))
               (+ x (* y (/ (- t x) a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -9.5e+29) {
		tmp = x + ((y - z) / (a / t));
	} else if (a <= -8.5e-120) {
		tmp = t_1;
	} else if (a <= -9.6e-150) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else if (a <= -5e-221) {
		tmp = t_1;
	} else if (a <= 4.7e-176) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 0.0115) {
		tmp = t + ((x - t) * (y / z));
	} else {
		tmp = x + (y * ((t - 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) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (a <= (-9.5d+29)) then
        tmp = x + ((y - z) / (a / t))
    else if (a <= (-8.5d-120)) then
        tmp = t_1
    else if (a <= (-9.6d-150)) then
        tmp = x * (((y - z) / (z - a)) + 1.0d0)
    else if (a <= (-5d-221)) then
        tmp = t_1
    else if (a <= 4.7d-176) then
        tmp = t + ((y * (x - t)) / z)
    else if (a <= 0.0115d0) then
        tmp = t + ((x - t) * (y / z))
    else
        tmp = x + (y * ((t - x) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -9.5e+29) {
		tmp = x + ((y - z) / (a / t));
	} else if (a <= -8.5e-120) {
		tmp = t_1;
	} else if (a <= -9.6e-150) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else if (a <= -5e-221) {
		tmp = t_1;
	} else if (a <= 4.7e-176) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 0.0115) {
		tmp = t + ((x - t) * (y / z));
	} else {
		tmp = x + (y * ((t - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if a <= -9.5e+29:
		tmp = x + ((y - z) / (a / t))
	elif a <= -8.5e-120:
		tmp = t_1
	elif a <= -9.6e-150:
		tmp = x * (((y - z) / (z - a)) + 1.0)
	elif a <= -5e-221:
		tmp = t_1
	elif a <= 4.7e-176:
		tmp = t + ((y * (x - t)) / z)
	elif a <= 0.0115:
		tmp = t + ((x - t) * (y / z))
	else:
		tmp = x + (y * ((t - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (a <= -9.5e+29)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / t)));
	elseif (a <= -8.5e-120)
		tmp = t_1;
	elseif (a <= -9.6e-150)
		tmp = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0));
	elseif (a <= -5e-221)
		tmp = t_1;
	elseif (a <= 4.7e-176)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	elseif (a <= 0.0115)
		tmp = Float64(t + Float64(Float64(x - t) * Float64(y / z)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (a <= -9.5e+29)
		tmp = x + ((y - z) / (a / t));
	elseif (a <= -8.5e-120)
		tmp = t_1;
	elseif (a <= -9.6e-150)
		tmp = x * (((y - z) / (z - a)) + 1.0);
	elseif (a <= -5e-221)
		tmp = t_1;
	elseif (a <= 4.7e-176)
		tmp = t + ((y * (x - t)) / z);
	elseif (a <= 0.0115)
		tmp = t + ((x - t) * (y / z));
	else
		tmp = x + (y * ((t - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.5e+29], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.5e-120], t$95$1, If[LessEqual[a, -9.6e-150], N[(x * N[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5e-221], t$95$1, If[LessEqual[a, 4.7e-176], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.0115], N[(t + N[(N[(x - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -9.5000000000000003e29

   1. Initial program 67.8%

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

      1. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

      1. clear-num 90.1%

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

      2. un-div-inv 90.3%

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

   6. Applied egg-rr 90.3%

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

   7. Taylor expanded in a around inf 79.3%

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

   8. Taylor expanded in t around inf 75.8%

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

   if -9.5000000000000003e29 < a < -8.50000000000000059e-120 or -9.6e-150 < a < -4.99999999999999996e-221

   1. Initial program 73.7%

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

      1. associate-/l* 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in x around 0 66.5%

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

      1. associate-/l* 76.3%

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

   7. Simplified 76.3%

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

   if -8.50000000000000059e-120 < a < -9.6e-150

   1. Initial program 70.5%

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

      1. associate-/l* 77.8%

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

   3. Simplified 77.8%

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

   5. Taylor expanded in x around inf 70.5%

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

      1. mul-1-neg 70.5%

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

      2. unsub-neg 70.5%

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

   7. Simplified 70.5%

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

   if -4.99999999999999996e-221 < a < 4.69999999999999984e-176

   1. Initial program 67.1%

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

      1. associate-/l* 67.2%

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

   3. Simplified 67.2%

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

   5. Taylor expanded in a around 0 66.7%

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

      1. associate-*r/ 66.7%

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

      2. associate-*r* 66.7%

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

      3. neg-mul-1 66.7%

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

      4. *-commutative 66.7%

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

   7. Simplified 66.7%

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

   8. Taylor expanded in y around 0 67.2%

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

      1. +-commutative 67.2%

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

      2. div-sub 67.3%

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

      3. associate-/l* 72.6%

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

      4. mul-1-neg 72.6%

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

      5. unsub-neg 72.6%

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

      6. associate-/l* 67.3%

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

   10. Simplified 67.3%

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

   11. Taylor expanded in z around inf 99.5%

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

   if 4.69999999999999984e-176 < a < 0.0115

   1. Initial program 62.1%

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

      1. associate-/l* 76.9%

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

   3. Simplified 76.9%

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

   5. Taylor expanded in a around 0 47.6%

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

      1. associate-*r/ 47.6%

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

      2. associate-*r* 47.6%

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

      3. neg-mul-1 47.6%

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

      4. *-commutative 47.6%

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

   7. Simplified 47.6%

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

   8. Taylor expanded in y around 0 60.3%

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

      1. +-commutative 60.3%

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

      2. div-sub 62.6%

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

      3. associate-/l* 58.4%

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

      4. mul-1-neg 58.4%

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

      5. unsub-neg 58.4%

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

      6. associate-/l* 62.6%

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

   10. Simplified 62.6%

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

   11. Taylor expanded in y around 0 72.1%

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

       1. div-sub 74.4%

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

   13. Simplified 74.4%

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

       1. clear-num 74.2%

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

       2. un-div-inv 74.3%

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

   15. Applied egg-rr 74.3%

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

       1. associate-/r/ 78.6%

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

   17. Simplified 78.6%

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

   if 0.0115 < a

   1. Initial program 67.6%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in z around 0 55.2%

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

      1. associate-/l* 70.8%

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

   7. Simplified 70.8%

      \[\leadsto \color{blue}{x + y \cdot \frac{t - x}{a}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-120}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{-150}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-221}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-176}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 0.0115:\\ \;\;\;\;t + \left(x - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(x - t\right)}{z}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-231}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-281}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-107}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 27000000000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- x t)) z)) (t_2 (* t (- 1.0 (/ y z)))))
   (if (<= a -1.9e+48)
     x
     (if (<= a -1e-231)
       t_2
       (if (<= a -1.1e-281)
         t_1
         (if (<= a 2.6e-107)
           t_2
           (if (<= a 1.25e-59) t_1 (if (<= a 27000000000.0) t_2 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (x - t)) / z;
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -1.9e+48) {
		tmp = x;
	} else if (a <= -1e-231) {
		tmp = t_2;
	} else if (a <= -1.1e-281) {
		tmp = t_1;
	} else if (a <= 2.6e-107) {
		tmp = t_2;
	} else if (a <= 1.25e-59) {
		tmp = t_1;
	} else if (a <= 27000000000.0) {
		tmp = t_2;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * (x - t)) / z
    t_2 = t * (1.0d0 - (y / z))
    if (a <= (-1.9d+48)) then
        tmp = x
    else if (a <= (-1d-231)) then
        tmp = t_2
    else if (a <= (-1.1d-281)) then
        tmp = t_1
    else if (a <= 2.6d-107) then
        tmp = t_2
    else if (a <= 1.25d-59) then
        tmp = t_1
    else if (a <= 27000000000.0d0) then
        tmp = t_2
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (x - t)) / z;
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -1.9e+48) {
		tmp = x;
	} else if (a <= -1e-231) {
		tmp = t_2;
	} else if (a <= -1.1e-281) {
		tmp = t_1;
	} else if (a <= 2.6e-107) {
		tmp = t_2;
	} else if (a <= 1.25e-59) {
		tmp = t_1;
	} else if (a <= 27000000000.0) {
		tmp = t_2;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (x - t)) / z
	t_2 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -1.9e+48:
		tmp = x
	elif a <= -1e-231:
		tmp = t_2
	elif a <= -1.1e-281:
		tmp = t_1
	elif a <= 2.6e-107:
		tmp = t_2
	elif a <= 1.25e-59:
		tmp = t_1
	elif a <= 27000000000.0:
		tmp = t_2
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(x - t)) / z)
	t_2 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -1.9e+48)
		tmp = x;
	elseif (a <= -1e-231)
		tmp = t_2;
	elseif (a <= -1.1e-281)
		tmp = t_1;
	elseif (a <= 2.6e-107)
		tmp = t_2;
	elseif (a <= 1.25e-59)
		tmp = t_1;
	elseif (a <= 27000000000.0)
		tmp = t_2;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (x - t)) / z;
	t_2 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -1.9e+48)
		tmp = x;
	elseif (a <= -1e-231)
		tmp = t_2;
	elseif (a <= -1.1e-281)
		tmp = t_1;
	elseif (a <= 2.6e-107)
		tmp = t_2;
	elseif (a <= 1.25e-59)
		tmp = t_1;
	elseif (a <= 27000000000.0)
		tmp = t_2;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.9e+48], x, If[LessEqual[a, -1e-231], t$95$2, If[LessEqual[a, -1.1e-281], t$95$1, If[LessEqual[a, 2.6e-107], t$95$2, If[LessEqual[a, 1.25e-59], t$95$1, If[LessEqual[a, 27000000000.0], t$95$2, x]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.9e48 or 2.7e10 < a

   1. Initial program 66.7%

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

      1. associate-/l* 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in a around inf 47.1%

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

   if -1.9e48 < a < -9.9999999999999999e-232 or -1.10000000000000002e-281 < a < 2.6000000000000001e-107 or 1.25e-59 < a < 2.7e10

   1. Initial program 66.7%

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

      1. associate-/l* 71.9%

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

   3. Simplified 71.9%

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

   5. Taylor expanded in a around 0 44.4%

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

      1. associate-*r/ 44.4%

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

      2. associate-*r* 44.4%

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

      3. neg-mul-1 44.4%

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

      4. *-commutative 44.4%

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

   7. Simplified 44.4%

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

   8. Taylor expanded in y around 0 55.5%

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

      1. +-commutative 55.5%

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

      2. div-sub 56.2%

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

      3. associate-/l* 51.1%

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

      4. mul-1-neg 51.1%

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

      5. unsub-neg 51.1%

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

      6. associate-/l* 56.2%

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

   10. Simplified 56.2%

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

   11. Taylor expanded in x around 0 51.9%

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

       1. *-rgt-identity 51.9%

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

       2. mul-1-neg 51.9%

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

       3. associate-/l* 57.7%

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

       4. distribute-rgt-neg-in 57.7%

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

       5. mul-1-neg 57.7%

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

       6. distribute-lft-in 57.7%

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

       7. mul-1-neg 57.7%

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

       8. unsub-neg 57.7%

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

   13. Simplified 57.7%

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

   if -9.9999999999999999e-232 < a < -1.10000000000000002e-281 or 2.6000000000000001e-107 < a < 1.25e-59

   1. Initial program 84.4%

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

      1. associate-/l* 79.1%

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

   3. Simplified 79.1%

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

   5. Taylor expanded in a around 0 79.4%

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

      1. associate-*r/ 79.4%

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

      2. associate-*r* 79.4%

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

      3. neg-mul-1 79.4%

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

      4. *-commutative 79.4%

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

   7. Simplified 79.4%

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

   8. Taylor expanded in y around -inf 84.2%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-231}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-281}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-107}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-59}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 27000000000:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(x - t\right)}{z}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -8.8 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-231}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-281}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-107}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 29500000000:\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- x t)) z)) (t_2 (* t (- 1.0 (/ y z)))))
   (if (<= a -8.8e+42)
     x
     (if (<= a -1e-231)
       t_2
       (if (<= a -1.1e-281)
         t_1
         (if (<= a 2.2e-107)
           t_2
           (if (<= a 1.25e-59)
             t_1
             (if (<= a 29500000000.0) (- t (* y (/ t z))) x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (x - t)) / z;
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -8.8e+42) {
		tmp = x;
	} else if (a <= -1e-231) {
		tmp = t_2;
	} else if (a <= -1.1e-281) {
		tmp = t_1;
	} else if (a <= 2.2e-107) {
		tmp = t_2;
	} else if (a <= 1.25e-59) {
		tmp = t_1;
	} else if (a <= 29500000000.0) {
		tmp = t - (y * (t / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * (x - t)) / z
    t_2 = t * (1.0d0 - (y / z))
    if (a <= (-8.8d+42)) then
        tmp = x
    else if (a <= (-1d-231)) then
        tmp = t_2
    else if (a <= (-1.1d-281)) then
        tmp = t_1
    else if (a <= 2.2d-107) then
        tmp = t_2
    else if (a <= 1.25d-59) then
        tmp = t_1
    else if (a <= 29500000000.0d0) then
        tmp = t - (y * (t / z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (x - t)) / z;
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -8.8e+42) {
		tmp = x;
	} else if (a <= -1e-231) {
		tmp = t_2;
	} else if (a <= -1.1e-281) {
		tmp = t_1;
	} else if (a <= 2.2e-107) {
		tmp = t_2;
	} else if (a <= 1.25e-59) {
		tmp = t_1;
	} else if (a <= 29500000000.0) {
		tmp = t - (y * (t / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (x - t)) / z
	t_2 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -8.8e+42:
		tmp = x
	elif a <= -1e-231:
		tmp = t_2
	elif a <= -1.1e-281:
		tmp = t_1
	elif a <= 2.2e-107:
		tmp = t_2
	elif a <= 1.25e-59:
		tmp = t_1
	elif a <= 29500000000.0:
		tmp = t - (y * (t / z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(x - t)) / z)
	t_2 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -8.8e+42)
		tmp = x;
	elseif (a <= -1e-231)
		tmp = t_2;
	elseif (a <= -1.1e-281)
		tmp = t_1;
	elseif (a <= 2.2e-107)
		tmp = t_2;
	elseif (a <= 1.25e-59)
		tmp = t_1;
	elseif (a <= 29500000000.0)
		tmp = Float64(t - Float64(y * Float64(t / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (x - t)) / z;
	t_2 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -8.8e+42)
		tmp = x;
	elseif (a <= -1e-231)
		tmp = t_2;
	elseif (a <= -1.1e-281)
		tmp = t_1;
	elseif (a <= 2.2e-107)
		tmp = t_2;
	elseif (a <= 1.25e-59)
		tmp = t_1;
	elseif (a <= 29500000000.0)
		tmp = t - (y * (t / z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.8e+42], x, If[LessEqual[a, -1e-231], t$95$2, If[LessEqual[a, -1.1e-281], t$95$1, If[LessEqual[a, 2.2e-107], t$95$2, If[LessEqual[a, 1.25e-59], t$95$1, If[LessEqual[a, 29500000000.0], N[(t - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.8000000000000005e42 or 2.95e10 < a

   1. Initial program 66.7%

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

      1. associate-/l* 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in a around inf 47.1%

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

   if -8.8000000000000005e42 < a < -9.9999999999999999e-232 or -1.10000000000000002e-281 < a < 2.20000000000000012e-107

   1. Initial program 70.2%

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

      1. associate-/l* 71.2%

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

   3. Simplified 71.2%

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

   5. Taylor expanded in a around 0 46.8%

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

      1. associate-*r/ 46.8%

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

      2. associate-*r* 46.8%

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

      3. neg-mul-1 46.8%

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

      4. *-commutative 46.8%

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

   7. Simplified 46.8%

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

   8. Taylor expanded in y around 0 53.9%

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

      1. +-commutative 53.9%

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

      2. div-sub 54.9%

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

      3. associate-/l* 51.3%

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

      4. mul-1-neg 51.3%

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

      5. unsub-neg 51.3%

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

      6. associate-/l* 54.9%

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

   10. Simplified 54.9%

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

   11. Taylor expanded in x around 0 52.6%

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

       1. *-rgt-identity 52.6%

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

       2. mul-1-neg 52.6%

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

       3. associate-/l* 57.7%

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

       4. distribute-rgt-neg-in 57.7%

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

       5. mul-1-neg 57.7%

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

       6. distribute-lft-in 57.7%

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

       7. mul-1-neg 57.7%

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

       8. unsub-neg 57.7%

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

   13. Simplified 57.7%

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

   if -9.9999999999999999e-232 < a < -1.10000000000000002e-281 or 2.20000000000000012e-107 < a < 1.25e-59

   1. Initial program 84.4%

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

      1. associate-/l* 79.1%

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

   3. Simplified 79.1%

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

   5. Taylor expanded in a around 0 79.4%

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

      1. associate-*r/ 79.4%

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

      2. associate-*r* 79.4%

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

      3. neg-mul-1 79.4%

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

      4. *-commutative 79.4%

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

   7. Simplified 79.4%

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

   8. Taylor expanded in y around -inf 84.2%

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

   if 1.25e-59 < a < 2.95e10

   1. Initial program 48.2%

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

      1. associate-/l* 75.5%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in a around 0 31.6%

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

      1. associate-*r/ 31.6%

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

      2. associate-*r* 31.6%

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

      3. neg-mul-1 31.6%

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

      4. *-commutative 31.6%

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

   7. Simplified 31.6%

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

   8. Taylor expanded in y around 0 63.7%

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

      1. +-commutative 63.7%

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

      2. div-sub 63.7%

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

      3. associate-/l* 50.1%

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

      4. mul-1-neg 50.1%

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

      5. unsub-neg 50.1%

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

      6. associate-/l* 63.7%

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

   10. Simplified 63.7%

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

   11. Taylor expanded in y around 0 73.7%

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

       1. div-sub 73.7%

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

   13. Simplified 73.7%

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

   14. Taylor expanded in x around 0 57.2%

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

       1. neg-mul-1 57.2%

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

       2. distribute-neg-frac2 57.2%

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

   16. Simplified 57.2%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-231}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-281}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-107}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-59}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 29500000000:\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -5 \cdot 10^{+158}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-80}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (* y (/ (- t x) (- a z)))))
   (if (<= y -5e+158)
     t_2
     (if (<= y 8.5e-161)
       t_1
       (if (<= y 4.6e-80) x (if (<= y 1.7e+47) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -5e+158) {
		tmp = t_2;
	} else if (y <= 8.5e-161) {
		tmp = t_1;
	} else if (y <= 4.6e-80) {
		tmp = x;
	} else if (y <= 1.7e+47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = y * ((t - x) / (a - z))
    if (y <= (-5d+158)) then
        tmp = t_2
    else if (y <= 8.5d-161) then
        tmp = t_1
    else if (y <= 4.6d-80) then
        tmp = x
    else if (y <= 1.7d+47) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -5e+158) {
		tmp = t_2;
	} else if (y <= 8.5e-161) {
		tmp = t_1;
	} else if (y <= 4.6e-80) {
		tmp = x;
	} else if (y <= 1.7e+47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = y * ((t - x) / (a - z))
	tmp = 0
	if y <= -5e+158:
		tmp = t_2
	elif y <= 8.5e-161:
		tmp = t_1
	elif y <= 4.6e-80:
		tmp = x
	elif y <= 1.7e+47:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (y <= -5e+158)
		tmp = t_2;
	elseif (y <= 8.5e-161)
		tmp = t_1;
	elseif (y <= 4.6e-80)
		tmp = x;
	elseif (y <= 1.7e+47)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (y <= -5e+158)
		tmp = t_2;
	elseif (y <= 8.5e-161)
		tmp = t_1;
	elseif (y <= 4.6e-80)
		tmp = x;
	elseif (y <= 1.7e+47)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+158], t$95$2, If[LessEqual[y, 8.5e-161], t$95$1, If[LessEqual[y, 4.6e-80], x, If[LessEqual[y, 1.7e+47], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9999999999999996e158 or 1.6999999999999999e47 < y

   1. Initial program 70.9%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in y around inf 80.2%

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

      1. div-sub 80.2%

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

   7. Simplified 80.2%

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

   if -4.9999999999999996e158 < y < 8.50000000000000054e-161 or 4.5999999999999996e-80 < y < 1.6999999999999999e47

   1. Initial program 64.9%

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

      1. associate-/l* 71.6%

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

   3. Simplified 71.6%

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

   5. Taylor expanded in x around 0 43.7%

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

      1. associate-/l* 57.3%

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

   7. Simplified 57.3%

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

   if 8.50000000000000054e-161 < y < 4.5999999999999996e-80

   1. Initial program 80.5%

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

      1. associate-/l* 74.4%

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

   3. Simplified 74.4%

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

   5. Taylor expanded in a around inf 55.7%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+158}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-161}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-80}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{+148}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 30000000000:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+208}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= a -2.1e+148)
     x
     (if (<= a -3.6e-118)
       t_1
       (if (<= a 30000000000.0)
         (- t (* y (/ (- t x) z)))
         (if (<= a 6.2e+208) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -2.1e+148) {
		tmp = x;
	} else if (a <= -3.6e-118) {
		tmp = t_1;
	} else if (a <= 30000000000.0) {
		tmp = t - (y * ((t - x) / z));
	} else if (a <= 6.2e+208) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (a <= (-2.1d+148)) then
        tmp = x
    else if (a <= (-3.6d-118)) then
        tmp = t_1
    else if (a <= 30000000000.0d0) then
        tmp = t - (y * ((t - x) / z))
    else if (a <= 6.2d+208) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -2.1e+148) {
		tmp = x;
	} else if (a <= -3.6e-118) {
		tmp = t_1;
	} else if (a <= 30000000000.0) {
		tmp = t - (y * ((t - x) / z));
	} else if (a <= 6.2e+208) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if a <= -2.1e+148:
		tmp = x
	elif a <= -3.6e-118:
		tmp = t_1
	elif a <= 30000000000.0:
		tmp = t - (y * ((t - x) / z))
	elif a <= 6.2e+208:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (a <= -2.1e+148)
		tmp = x;
	elseif (a <= -3.6e-118)
		tmp = t_1;
	elseif (a <= 30000000000.0)
		tmp = Float64(t - Float64(y * Float64(Float64(t - x) / z)));
	elseif (a <= 6.2e+208)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (a <= -2.1e+148)
		tmp = x;
	elseif (a <= -3.6e-118)
		tmp = t_1;
	elseif (a <= 30000000000.0)
		tmp = t - (y * ((t - x) / z));
	elseif (a <= 6.2e+208)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.1e+148], x, If[LessEqual[a, -3.6e-118], t$95$1, If[LessEqual[a, 30000000000.0], N[(t - N[(y * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e+208], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.09999999999999999e148 or 6.19999999999999961e208 < a

   1. Initial program 65.2%

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

      1. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in a around inf 60.3%

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

   if -2.09999999999999999e148 < a < -3.6000000000000002e-118 or 3e10 < a < 6.19999999999999961e208

   1. Initial program 67.4%

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

      1. associate-/l* 80.5%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in x around 0 39.7%

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

      1. associate-/l* 59.3%

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

   7. Simplified 59.3%

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

   if -3.6000000000000002e-118 < a < 3e10

   1. Initial program 69.7%

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

      1. associate-/l* 73.0%

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

   3. Simplified 73.0%

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

   5. Taylor expanded in a around 0 53.2%

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

      1. associate-*r/ 53.2%

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

      2. associate-*r* 53.2%

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

      3. neg-mul-1 53.2%

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

      4. *-commutative 53.2%

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

   7. Simplified 53.2%

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

   8. Taylor expanded in y around 0 61.4%

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

      1. +-commutative 61.4%

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

      2. div-sub 62.3%

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

      3. associate-/l* 58.9%

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

      4. mul-1-neg 58.9%

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

      5. unsub-neg 58.9%

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

      6. associate-/l* 62.3%

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

   10. Simplified 62.3%

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

   11. Taylor expanded in y around 0 75.1%

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

       1. div-sub 76.0%

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

   13. Simplified 76.0%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+148}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-118}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 30000000000:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+208}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+145}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 55000000000:\\ \;\;\;\;t + \left(x - t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+209}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= a -1.8e+145)
     x
     (if (<= a -2e-121)
       t_1
       (if (<= a 55000000000.0)
         (+ t (* (- x t) (/ y z)))
         (if (<= a 1.6e+209) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -1.8e+145) {
		tmp = x;
	} else if (a <= -2e-121) {
		tmp = t_1;
	} else if (a <= 55000000000.0) {
		tmp = t + ((x - t) * (y / z));
	} else if (a <= 1.6e+209) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (a <= (-1.8d+145)) then
        tmp = x
    else if (a <= (-2d-121)) then
        tmp = t_1
    else if (a <= 55000000000.0d0) then
        tmp = t + ((x - t) * (y / z))
    else if (a <= 1.6d+209) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -1.8e+145) {
		tmp = x;
	} else if (a <= -2e-121) {
		tmp = t_1;
	} else if (a <= 55000000000.0) {
		tmp = t + ((x - t) * (y / z));
	} else if (a <= 1.6e+209) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if a <= -1.8e+145:
		tmp = x
	elif a <= -2e-121:
		tmp = t_1
	elif a <= 55000000000.0:
		tmp = t + ((x - t) * (y / z))
	elif a <= 1.6e+209:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (a <= -1.8e+145)
		tmp = x;
	elseif (a <= -2e-121)
		tmp = t_1;
	elseif (a <= 55000000000.0)
		tmp = Float64(t + Float64(Float64(x - t) * Float64(y / z)));
	elseif (a <= 1.6e+209)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (a <= -1.8e+145)
		tmp = x;
	elseif (a <= -2e-121)
		tmp = t_1;
	elseif (a <= 55000000000.0)
		tmp = t + ((x - t) * (y / z));
	elseif (a <= 1.6e+209)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e+145], x, If[LessEqual[a, -2e-121], t$95$1, If[LessEqual[a, 55000000000.0], N[(t + N[(N[(x - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+209], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.79999999999999987e145 or 1.6e209 < a

   1. Initial program 65.2%

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

      1. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in a around inf 60.3%

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

   if -1.79999999999999987e145 < a < -2e-121 or 5.5e10 < a < 1.6e209

   1. Initial program 67.4%

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

      1. associate-/l* 80.5%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in x around 0 39.7%

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

      1. associate-/l* 59.3%

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

   7. Simplified 59.3%

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

   if -2e-121 < a < 5.5e10

   1. Initial program 69.7%

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

      1. associate-/l* 73.0%

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

   3. Simplified 73.0%

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

   5. Taylor expanded in a around 0 53.2%

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

      1. associate-*r/ 53.2%

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

      2. associate-*r* 53.2%

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

      3. neg-mul-1 53.2%

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

      4. *-commutative 53.2%

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

   7. Simplified 53.2%

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

   8. Taylor expanded in y around 0 61.4%

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

      1. +-commutative 61.4%

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

      2. div-sub 62.3%

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

      3. associate-/l* 58.9%

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

      4. mul-1-neg 58.9%

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

      5. unsub-neg 58.9%

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

      6. associate-/l* 62.3%

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

   10. Simplified 62.3%

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

   11. Taylor expanded in y around 0 75.1%

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

       1. div-sub 76.0%

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

   13. Simplified 76.0%

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

       1. clear-num 75.9%

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

       2. un-div-inv 76.0%

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

   15. Applied egg-rr 76.0%

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

       1. associate-/r/ 78.3%

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

   17. Simplified 78.3%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+145}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-121}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 55000000000:\\ \;\;\;\;t + \left(x - t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+209}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -1.42 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-59}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 14000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -1.42e+48)
     x
     (if (<= a 1.75e-107)
       t_1
       (if (<= a 1.25e-59) (/ (* x y) z) (if (<= a 14000000.0) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -1.42e+48) {
		tmp = x;
	} else if (a <= 1.75e-107) {
		tmp = t_1;
	} else if (a <= 1.25e-59) {
		tmp = (x * y) / z;
	} else if (a <= 14000000.0) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (a <= (-1.42d+48)) then
        tmp = x
    else if (a <= 1.75d-107) then
        tmp = t_1
    else if (a <= 1.25d-59) then
        tmp = (x * y) / z
    else if (a <= 14000000.0d0) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -1.42e+48) {
		tmp = x;
	} else if (a <= 1.75e-107) {
		tmp = t_1;
	} else if (a <= 1.25e-59) {
		tmp = (x * y) / z;
	} else if (a <= 14000000.0) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -1.42e+48:
		tmp = x
	elif a <= 1.75e-107:
		tmp = t_1
	elif a <= 1.25e-59:
		tmp = (x * y) / z
	elif a <= 14000000.0:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -1.42e+48)
		tmp = x;
	elseif (a <= 1.75e-107)
		tmp = t_1;
	elseif (a <= 1.25e-59)
		tmp = Float64(Float64(x * y) / z);
	elseif (a <= 14000000.0)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -1.42e+48)
		tmp = x;
	elseif (a <= 1.75e-107)
		tmp = t_1;
	elseif (a <= 1.25e-59)
		tmp = (x * y) / z;
	elseif (a <= 14000000.0)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.42e+48], x, If[LessEqual[a, 1.75e-107], t$95$1, If[LessEqual[a, 1.25e-59], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 14000000.0], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.42e48 or 1.4e7 < a

   1. Initial program 66.7%

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

      1. associate-/l* 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in a around inf 47.1%

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

   if -1.42e48 < a < 1.74999999999999993e-107 or 1.25e-59 < a < 1.4e7

   1. Initial program 68.0%

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

      1. associate-/l* 72.1%

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

   3. Simplified 72.1%

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

   5. Taylor expanded in a around 0 47.0%

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

      1. associate-*r/ 47.0%

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

      2. associate-*r* 47.0%

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

      3. neg-mul-1 47.0%

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

      4. *-commutative 47.0%

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

   7. Simplified 47.0%

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

   8. Taylor expanded in y around 0 56.7%

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

      1. +-commutative 56.7%

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

      2. div-sub 57.5%

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

      3. associate-/l* 53.3%

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

      4. mul-1-neg 53.3%

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

      5. unsub-neg 53.3%

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

      6. associate-/l* 57.5%

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

   10. Simplified 57.5%

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

   11. Taylor expanded in x around 0 51.7%

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

       1. *-rgt-identity 51.7%

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

       2. mul-1-neg 51.7%

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

       3. associate-/l* 57.0%

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

       4. distribute-rgt-neg-in 57.0%

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

       5. mul-1-neg 57.0%

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

       6. distribute-lft-in 57.0%

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

       7. mul-1-neg 57.0%

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

       8. unsub-neg 57.0%

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

   13. Simplified 57.0%

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

   if 1.74999999999999993e-107 < a < 1.25e-59

   1. Initial program 81.4%

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

      1. associate-/l* 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in a around 0 72.5%

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

      1. associate-*r/ 72.5%

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

      2. associate-*r* 72.5%

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

      3. neg-mul-1 72.5%

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

      4. *-commutative 72.5%

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

   7. Simplified 72.5%

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

   8. Taylor expanded in x around inf 71.8%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.42 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-107}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-59}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 14000000:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 70.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-122}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 0.00235:\\ \;\;\;\;t + \left(x - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- t x) a)))))
   (if (<= a -2.8e+27)
     t_1
     (if (<= a -5e-122)
       (* t (/ (- y z) (- a z)))
       (if (<= a 0.00235) (+ t (* (- x t) (/ y z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -2.8e+27) {
		tmp = t_1;
	} else if (a <= -5e-122) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 0.00235) {
		tmp = t + ((x - t) * (y / z));
	} 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 * ((t - x) / a))
    if (a <= (-2.8d+27)) then
        tmp = t_1
    else if (a <= (-5d-122)) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= 0.00235d0) then
        tmp = t + ((x - t) * (y / z))
    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 * ((t - x) / a));
	double tmp;
	if (a <= -2.8e+27) {
		tmp = t_1;
	} else if (a <= -5e-122) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 0.00235) {
		tmp = t + ((x - t) * (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((t - x) / a))
	tmp = 0
	if a <= -2.8e+27:
		tmp = t_1
	elif a <= -5e-122:
		tmp = t * ((y - z) / (a - z))
	elif a <= 0.00235:
		tmp = t + ((x - t) * (y / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -2.8e+27)
		tmp = t_1;
	elseif (a <= -5e-122)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= 0.00235)
		tmp = Float64(t + Float64(Float64(x - t) * Float64(y / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((t - x) / a));
	tmp = 0.0;
	if (a <= -2.8e+27)
		tmp = t_1;
	elseif (a <= -5e-122)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= 0.00235)
		tmp = t + ((x - t) * (y / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.8e+27], t$95$1, If[LessEqual[a, -5e-122], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.00235], N[(t + N[(N[(x - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.7999999999999999e27 or 0.00235000000000000009 < a

   1. Initial program 67.7%

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

      1. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in z around 0 58.7%

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

      1. associate-/l* 71.7%

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

   7. Simplified 71.7%

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

   if -2.7999999999999999e27 < a < -4.9999999999999999e-122

   1. Initial program 68.6%

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

      1. associate-/l* 68.8%

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

   3. Simplified 68.8%

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

   5. Taylor expanded in x around 0 62.3%

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

      1. associate-/l* 72.3%

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

   7. Simplified 72.3%

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

   if -4.9999999999999999e-122 < a < 0.00235000000000000009

   1. Initial program 68.1%

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

      1. associate-/l* 72.4%

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

   3. Simplified 72.4%

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

   5. Taylor expanded in a around 0 53.3%

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

      1. associate-*r/ 53.3%

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

      2. associate-*r* 53.3%

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

      3. neg-mul-1 53.3%

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

      4. *-commutative 53.3%

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

   7. Simplified 53.3%

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

   8. Taylor expanded in y around 0 61.9%

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

      1. +-commutative 61.9%

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

      2. div-sub 62.9%

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

      3. associate-/l* 59.3%

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

      4. mul-1-neg 59.3%

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

      5. unsub-neg 59.3%

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

      6. associate-/l* 62.9%

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

   10. Simplified 62.9%

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

   11. Taylor expanded in y around 0 76.4%

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

       1. div-sub 77.4%

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

   13. Simplified 77.4%

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

       1. clear-num 77.3%

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

       2. un-div-inv 77.3%

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

   15. Applied egg-rr 77.3%

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

       1. associate-/r/ 79.8%

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

   17. Simplified 79.8%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+27}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-122}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 0.00235:\\ \;\;\;\;t + \left(x - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 70.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-117}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 0.0054:\\ \;\;\;\;t + \left(x - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.6e+30)
   (+ x (/ (- y z) (/ a t)))
   (if (<= a -3.7e-117)
     (* t (/ (- y z) (- a z)))
     (if (<= a 0.0054) (+ t (* (- x t) (/ y z))) (+ x (* y (/ (- t x) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e+30) {
		tmp = x + ((y - z) / (a / t));
	} else if (a <= -3.7e-117) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 0.0054) {
		tmp = t + ((x - t) * (y / z));
	} else {
		tmp = x + (y * ((t - 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 (a <= (-1.6d+30)) then
        tmp = x + ((y - z) / (a / t))
    else if (a <= (-3.7d-117)) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= 0.0054d0) then
        tmp = t + ((x - t) * (y / z))
    else
        tmp = x + (y * ((t - 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 (a <= -1.6e+30) {
		tmp = x + ((y - z) / (a / t));
	} else if (a <= -3.7e-117) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 0.0054) {
		tmp = t + ((x - t) * (y / z));
	} else {
		tmp = x + (y * ((t - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.6e+30:
		tmp = x + ((y - z) / (a / t))
	elif a <= -3.7e-117:
		tmp = t * ((y - z) / (a - z))
	elif a <= 0.0054:
		tmp = t + ((x - t) * (y / z))
	else:
		tmp = x + (y * ((t - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.6e+30)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / t)));
	elseif (a <= -3.7e-117)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= 0.0054)
		tmp = Float64(t + Float64(Float64(x - t) * Float64(y / z)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.6e+30)
		tmp = x + ((y - z) / (a / t));
	elseif (a <= -3.7e-117)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= 0.0054)
		tmp = t + ((x - t) * (y / z));
	else
		tmp = x + (y * ((t - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.6e+30], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.7e-117], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.0054], N[(t + N[(N[(x - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.59999999999999986e30

   1. Initial program 67.8%

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

      1. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

      1. clear-num 90.1%

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

      2. un-div-inv 90.3%

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

   6. Applied egg-rr 90.3%

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

   7. Taylor expanded in a around inf 79.3%

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

   8. Taylor expanded in t around inf 75.8%

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

   if -1.59999999999999986e30 < a < -3.7000000000000002e-117

   1. Initial program 68.6%

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

      1. associate-/l* 68.8%

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

   3. Simplified 68.8%

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

   5. Taylor expanded in x around 0 62.3%

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

      1. associate-/l* 72.3%

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

   7. Simplified 72.3%

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

   if -3.7000000000000002e-117 < a < 0.0054000000000000003

   1. Initial program 68.1%

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

      1. associate-/l* 72.4%

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

   3. Simplified 72.4%

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

   5. Taylor expanded in a around 0 53.3%

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

      1. associate-*r/ 53.3%

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

      2. associate-*r* 53.3%

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

      3. neg-mul-1 53.3%

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

      4. *-commutative 53.3%

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

   7. Simplified 53.3%

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

   8. Taylor expanded in y around 0 61.9%

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

      1. +-commutative 61.9%

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

      2. div-sub 62.9%

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

      3. associate-/l* 59.3%

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

      4. mul-1-neg 59.3%

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

      5. unsub-neg 59.3%

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

      6. associate-/l* 62.9%

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

   10. Simplified 62.9%

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

   11. Taylor expanded in y around 0 76.4%

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

       1. div-sub 77.4%

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

   13. Simplified 77.4%

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

       1. clear-num 77.3%

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

       2. un-div-inv 77.3%

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

   15. Applied egg-rr 77.3%

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

       1. associate-/r/ 79.8%

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

   17. Simplified 79.8%

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

   if 0.0054000000000000003 < a

   1. Initial program 67.6%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in z around 0 55.2%

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

      1. associate-/l* 70.8%

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

   7. Simplified 70.8%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-117}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 0.0054:\\ \;\;\;\;t + \left(x - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 82.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-222} \lor \neg \left(a \leq 9.5 \cdot 10^{-51}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -9.5e-222) (not (<= a 9.5e-51)))
   (+ x (* (- y z) (/ (- t x) (- a z))))
   (+ t (/ (* (- t x) (- a y)) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -9.5e-222) || !(a <= 9.5e-51)) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-9.5d-222)) .or. (.not. (a <= 9.5d-51))) then
        tmp = x + ((y - z) * ((t - x) / (a - z)))
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -9.5e-222) || !(a <= 9.5e-51)) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -9.5e-222) or not (a <= 9.5e-51):
		tmp = x + ((y - z) * ((t - x) / (a - z)))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -9.5e-222) || !(a <= 9.5e-51))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -9.5e-222) || ~((a <= 9.5e-51)))
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -9.5e-222], N[Not[LessEqual[a, 9.5e-51]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -9.5000000000000002e-222 or 9.4999999999999998e-51 < a

   1. Initial program 67.8%

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

      1. associate-/l* 83.3%

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

   3. Simplified 83.3%

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

   if -9.5000000000000002e-222 < a < 9.4999999999999998e-51

   1. Initial program 68.3%

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

      1. associate-/l* 71.2%

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

   3. Simplified 71.2%

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

   5. Taylor expanded in z around inf 90.5%

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

      1. associate--l+ 90.5%

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

      2. associate-*r/ 90.5%

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

      3. associate-*r/ 90.5%

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

      4. mul-1-neg 90.5%

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

      5. div-sub 90.5%

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

      6. mul-1-neg 90.5%

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

      7. distribute-lft-out-- 90.5%

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

      8. associate-*r/ 90.5%

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

      9. mul-1-neg 90.5%

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

      10. unsub-neg 90.5%

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

      11. distribute-rgt-out-- 90.5%

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

   7. Simplified 90.5%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-222} \lor \neg \left(a \leq 9.5 \cdot 10^{-51}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 37.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+46}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-291}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+141}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.2e+46)
   t
   (if (<= z 1.4e-291) (* t (/ y a)) (if (<= z 2.2e+141) x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+46) {
		tmp = t;
	} else if (z <= 1.4e-291) {
		tmp = t * (y / a);
	} else if (z <= 2.2e+141) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-5.2d+46)) then
        tmp = t
    else if (z <= 1.4d-291) then
        tmp = t * (y / a)
    else if (z <= 2.2d+141) then
        tmp = x
    else
        tmp = 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 (z <= -5.2e+46) {
		tmp = t;
	} else if (z <= 1.4e-291) {
		tmp = t * (y / a);
	} else if (z <= 2.2e+141) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.2e+46:
		tmp = t
	elif z <= 1.4e-291:
		tmp = t * (y / a)
	elif z <= 2.2e+141:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.2e+46)
		tmp = t;
	elseif (z <= 1.4e-291)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 2.2e+141)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.2e+46)
		tmp = t;
	elseif (z <= 1.4e-291)
		tmp = t * (y / a);
	elseif (z <= 2.2e+141)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.2e+46], t, If[LessEqual[z, 1.4e-291], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+141], x, t]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.20000000000000027e46 or 2.2e141 < z

   1. Initial program 37.8%

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

      1. associate-/l* 66.1%

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

   3. Simplified 66.1%

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

   5. Taylor expanded in z around inf 50.7%

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

   if -5.20000000000000027e46 < z < 1.4e-291

   1. Initial program 87.6%

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

      1. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in x around 0 45.2%

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

   6. Taylor expanded in z around 0 25.6%

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

      1. associate-/l* 34.0%

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

   8. Simplified 34.0%

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

   if 1.4e-291 < z < 2.2e141

   1. Initial program 84.1%

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

      1. associate-/l* 89.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in a around inf 36.3%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+46}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-291}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+141}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 39.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.9 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 23000000000:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.9e+40) x (if (<= a 23000000000.0) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.9e+40) {
		tmp = x;
	} else if (a <= 23000000000.0) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.9d+40)) then
        tmp = x
    else if (a <= 23000000000.0d0) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.9e+40) {
		tmp = x;
	} else if (a <= 23000000000.0) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.9e+40:
		tmp = x
	elif a <= 23000000000.0:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.9e+40)
		tmp = x;
	elseif (a <= 23000000000.0)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.9e+40)
		tmp = x;
	elseif (a <= 23000000000.0)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.9e+40], x, If[LessEqual[a, 23000000000.0], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -6.9000000000000003e40 or 2.3e10 < a

   1. Initial program 66.7%

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

      1. associate-/l* 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in a around inf 47.1%

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

   if -6.9000000000000003e40 < a < 2.3e10

   1. Initial program 68.9%

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

      1. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in z around inf 34.4%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.9 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 23000000000:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 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 68.0%

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

   1. associate-/l* 80.3%

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

3. Simplified 80.3%

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

5. Taylor expanded in a around 0 32.1%

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

   1. associate-*r/ 32.1%

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

   2. associate-*r* 32.1%

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

   3. neg-mul-1 32.1%

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

   4. *-commutative 32.1%

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

7. Simplified 32.1%

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

8. Taylor expanded in t around 0 17.2%

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

   1. *-commutative 17.2%

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

10. Simplified 17.2%

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

11. Taylor expanded in y around 0 2.7%

    \[\leadsto \color{blue}{x + -1 \cdot x} \]
12. Step-by-step derivation

    1. distribute-rgt1-in 2.7%

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

    2. metadata-eval 2.7%

       \[\leadsto \color{blue}{0} \cdot x \]

    3. mul0-lft 2.7%

       \[\leadsto \color{blue}{0} \]

13. Simplified 2.7%

    \[\leadsto \color{blue}{0} \]

14. Final simplification 2.7%

    \[\leadsto 0 \]
15. Add Preprocessing

Alternative 20: 25.5% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.0%

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

   1. associate-/l* 80.3%

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

3. Simplified 80.3%

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

5. Taylor expanded in z around inf 25.9%

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

6. Final simplification 25.9%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 83.7% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024077 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :alt
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

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