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

Percentage Accurate: 67.0% → 90.5%

Time: 17.0s

Alternatives: 16

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: 67.0% 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: 90.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-272} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -5e-272) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (+ 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 <= -5e-272) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} 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 <= -5e-272) || !(t_1 <= 0.0))
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return 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, -5e-272], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $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))) < -4.99999999999999982e-272 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 70.1%

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

      1. +-commutative 70.1%

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

      2. *-commutative 70.1%

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

      3. associate-/l* 91.7%

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

      4. fma-define 91.7%

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

   3. Simplified 91.7%

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

   if -4.99999999999999982e-272 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.1%

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

      1. associate-/l* 3.9%

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

   3. Simplified 3.9%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   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 99.7%

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

      6. mul-1-neg 99.7%

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

      7. distribute-lft-out-- 99.7%

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

      8. associate-*r/ 99.7%

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

      9. mul-1-neg 99.7%

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

      10. unsub-neg 99.7%

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

      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 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -5 \cdot 10^{-272} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-272}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-305}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 10^{+267}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -5e-272)
       t_2
       (if (<= t_2 5e-305)
         (+ t (/ (* (- t x) (- a y)) z))
         (if (<= t_2 1e+267) 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 <= -5e-272) {
		tmp = t_2;
	} else if (t_2 <= 5e-305) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 1e+267) {
		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 <= -5e-272) {
		tmp = t_2;
	} else if (t_2 <= 5e-305) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 1e+267) {
		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 <= -5e-272:
		tmp = t_2
	elif t_2 <= 5e-305:
		tmp = t + (((t - x) * (a - y)) / z)
	elif t_2 <= 1e+267:
		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 <= -5e-272)
		tmp = t_2;
	elseif (t_2 <= 5e-305)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (t_2 <= 1e+267)
		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 <= -5e-272)
		tmp = t_2;
	elseif (t_2 <= 5e-305)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (t_2 <= 1e+267)
		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, -5e-272], t$95$2, If[LessEqual[t$95$2, 5e-305], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+267], 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 9.9999999999999997e266 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 36.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.99999999999999982e-272 or 4.99999999999999985e-305 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 9.9999999999999997e266

   1. Initial program 98.6%

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

   if -4.99999999999999982e-272 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 4.99999999999999985e-305

   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* 7.9%

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

   3. Simplified 7.9%

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

   5. Taylor expanded in z around inf 95.9%

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

      1. associate--l+ 95.9%

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

      2. associate-*r/ 95.9%

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

      3. associate-*r/ 95.9%

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

      4. mul-1-neg 95.9%

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

      5. div-sub 95.8%

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

      6. mul-1-neg 95.8%

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

      7. distribute-lft-out-- 95.8%

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

      8. associate-*r/ 95.8%

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

      9. mul-1-neg 95.8%

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

      10. unsub-neg 95.8%

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

      11. distribute-rgt-out-- 95.9%

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

   7. Simplified 95.9%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -\infty:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -5 \cdot 10^{-272}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 5 \cdot 10^{-305}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 10^{+267}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-272} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -5e-272) (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 <= -5e-272) || !(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 <= (-5d-272)) .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 <= -5e-272) || !(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 <= -5e-272) 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 <= -5e-272) || !(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 <= -5e-272) || ~((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, -5e-272], 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))) < -4.99999999999999982e-272 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 70.1%

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

      1. associate-/l* 85.2%

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

   3. Simplified 85.2%

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

      1. *-commutative 85.2%

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

      2. associate-*l/ 70.1%

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

      3. associate-*r/ 91.7%

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

      4. clear-num 91.3%

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

      5. un-div-inv 91.4%

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

   6. Applied egg-rr 91.4%

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

   if -4.99999999999999982e-272 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.1%

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

      1. associate-/l* 3.9%

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

   3. Simplified 3.9%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   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 99.7%

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

      6. mul-1-neg 99.7%

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

      7. distribute-lft-out-- 99.7%

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

      8. associate-*r/ 99.7%

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

      9. mul-1-neg 99.7%

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

      10. unsub-neg 99.7%

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

      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 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -5 \cdot 10^{-272} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+175}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+253}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.1e+175)
   (* t (/ (- y z) (- a z)))
   (if (<= z 7.4e+253)
     (+ 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 (z <= -1.1e+175) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 7.4e+253) {
		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 (z <= (-1.1d+175)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 7.4d+253) 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 (z <= -1.1e+175) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 7.4e+253) {
		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 z <= -1.1e+175:
		tmp = t * ((y - z) / (a - z))
	elif z <= 7.4e+253:
		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 (z <= -1.1e+175)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 7.4e+253)
		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 (z <= -1.1e+175)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 7.4e+253)
		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[LessEqual[z, -1.1e+175], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.4e+253], 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 3 regimes

2. if z < -1.1e175

   1. Initial program 33.9%

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

      1. associate-/l* 49.6%

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

   3. Simplified 49.6%

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

   5. Taylor expanded in x around 0 44.3%

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

      1. associate-/l* 79.9%

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

   7. Simplified 79.9%

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

   if -1.1e175 < z < 7.40000000000000057e253

   1. Initial program 71.3%

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

      1. associate-/l* 84.8%

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

   3. Simplified 84.8%

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

   if 7.40000000000000057e253 < z

   1. Initial program 22.3%

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

      1. associate-/l* 35.7%

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

   3. Simplified 35.7%

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

   5. Taylor expanded in z around inf 80.6%

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

      1. associate--l+ 80.6%

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

      2. associate-*r/ 80.6%

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

      3. associate-*r/ 80.6%

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

      4. mul-1-neg 80.6%

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

      5. div-sub 80.6%

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

      6. mul-1-neg 80.6%

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

      7. distribute-lft-out-- 80.6%

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

      8. associate-*r/ 80.6%

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

      9. mul-1-neg 80.6%

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

      10. unsub-neg 80.6%

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

      11. distribute-rgt-out-- 80.6%

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

   7. Simplified 80.6%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+175}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+253}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 39.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+86}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.2e+29)
   (/ t (/ a (- y z)))
   (if (<= t 1.4e+35)
     (* x (- 1.0 (/ y a)))
     (if (<= t 1.55e+86) t (* t (/ (- y z) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.2e+29) {
		tmp = t / (a / (y - z));
	} else if (t <= 1.4e+35) {
		tmp = x * (1.0 - (y / a));
	} else if (t <= 1.55e+86) {
		tmp = t;
	} else {
		tmp = t * ((y - z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-6.2d+29)) then
        tmp = t / (a / (y - z))
    else if (t <= 1.4d+35) then
        tmp = x * (1.0d0 - (y / a))
    else if (t <= 1.55d+86) then
        tmp = t
    else
        tmp = t * ((y - z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.2e+29) {
		tmp = t / (a / (y - z));
	} else if (t <= 1.4e+35) {
		tmp = x * (1.0 - (y / a));
	} else if (t <= 1.55e+86) {
		tmp = t;
	} else {
		tmp = t * ((y - z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.2e+29:
		tmp = t / (a / (y - z))
	elif t <= 1.4e+35:
		tmp = x * (1.0 - (y / a))
	elif t <= 1.55e+86:
		tmp = t
	else:
		tmp = t * ((y - z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.2e+29)
		tmp = Float64(t / Float64(a / Float64(y - z)));
	elseif (t <= 1.4e+35)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (t <= 1.55e+86)
		tmp = t;
	else
		tmp = Float64(t * Float64(Float64(y - z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.2e+29)
		tmp = t / (a / (y - z));
	elseif (t <= 1.4e+35)
		tmp = x * (1.0 - (y / a));
	elseif (t <= 1.55e+86)
		tmp = t;
	else
		tmp = t * ((y - z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.2e+29], N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+35], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e+86], t, N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.1999999999999998e29

   1. Initial program 61.6%

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

      1. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in x around 0 50.4%

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

   6. Taylor expanded in a around inf 41.2%

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

      1. associate-/l* 49.6%

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

   8. Simplified 49.6%

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

      1. clear-num 49.6%

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

      2. un-div-inv 49.7%

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

   10. Applied egg-rr 49.7%

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

   if -6.1999999999999998e29 < t < 1.39999999999999999e35

   1. Initial program 69.5%

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

      1. associate-/l* 68.3%

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

   3. Simplified 68.3%

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

      1. *-commutative 68.3%

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

      2. associate-*l/ 69.5%

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

      3. associate-*r/ 75.1%

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

      4. clear-num 75.1%

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

      5. un-div-inv 75.1%

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

   6. Applied egg-rr 75.1%

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

   7. Taylor expanded in z around 0 50.1%

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

   8. Taylor expanded in x around inf 44.2%

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

      1. mul-1-neg 44.2%

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

      2. unsub-neg 44.2%

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

   10. Simplified 44.2%

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

   if 1.39999999999999999e35 < t < 1.5500000000000001e86

   1. Initial program 47.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 z around inf 61.0%

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

   if 1.5500000000000001e86 < t

   1. Initial program 59.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. Taylor expanded in x around 0 48.4%

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

   6. Taylor expanded in a around inf 37.7%

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

      1. associate-/l* 56.9%

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

   8. Simplified 56.9%

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

Alternative 6: 39.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ \mathbf{if}\;t \leq -5.9 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+86}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) a))))
   (if (<= t -5.9e+29)
     t_1
     (if (<= t 7.2e+34) (* x (- 1.0 (/ y a))) (if (<= t 1.15e+86) t t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / a);
	double tmp;
	if (t <= -5.9e+29) {
		tmp = t_1;
	} else if (t <= 7.2e+34) {
		tmp = x * (1.0 - (y / a));
	} else if (t <= 1.15e+86) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / a)
    if (t <= (-5.9d+29)) then
        tmp = t_1
    else if (t <= 7.2d+34) then
        tmp = x * (1.0d0 - (y / a))
    else if (t <= 1.15d+86) then
        tmp = t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / a);
	double tmp;
	if (t <= -5.9e+29) {
		tmp = t_1;
	} else if (t <= 7.2e+34) {
		tmp = x * (1.0 - (y / a));
	} else if (t <= 1.15e+86) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / a)
	tmp = 0
	if t <= -5.9e+29:
		tmp = t_1
	elif t <= 7.2e+34:
		tmp = x * (1.0 - (y / a))
	elif t <= 1.15e+86:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / a))
	tmp = 0.0
	if (t <= -5.9e+29)
		tmp = t_1;
	elseif (t <= 7.2e+34)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (t <= 1.15e+86)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / a);
	tmp = 0.0;
	if (t <= -5.9e+29)
		tmp = t_1;
	elseif (t <= 7.2e+34)
		tmp = x * (1.0 - (y / a));
	elseif (t <= 1.15e+86)
		tmp = t;
	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] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.9e+29], t$95$1, If[LessEqual[t, 7.2e+34], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+86], t, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.8999999999999999e29 or 1.14999999999999995e86 < t

   1. Initial program 60.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 x around 0 49.4%

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

   6. Taylor expanded in a around inf 39.5%

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

      1. associate-/l* 53.2%

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

   8. Simplified 53.2%

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

   if -5.8999999999999999e29 < t < 7.2000000000000001e34

   1. Initial program 69.5%

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

      1. associate-/l* 68.3%

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

   3. Simplified 68.3%

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

      1. *-commutative 68.3%

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

      2. associate-*l/ 69.5%

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

      3. associate-*r/ 75.1%

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

      4. clear-num 75.1%

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

      5. un-div-inv 75.1%

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

   6. Applied egg-rr 75.1%

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

   7. Taylor expanded in z around 0 50.1%

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

   8. Taylor expanded in x around inf 44.2%

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

      1. mul-1-neg 44.2%

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

      2. unsub-neg 44.2%

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

   10. Simplified 44.2%

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

   if 7.2000000000000001e34 < t < 1.14999999999999995e86

   1. Initial program 47.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 z around inf 61.0%

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

Alternative 7: 66.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+147}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+101}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.8e+147)
   (* t (/ (- y z) (- a z)))
   (if (<= z 1.3e+101)
     (+ x (* (- t x) (/ (- y z) a)))
     (/ t (/ (- a z) (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e+147) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 1.3e+101) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else {
		tmp = t / ((a - z) / (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 (z <= (-8.8d+147)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 1.3d+101) then
        tmp = x + ((t - x) * ((y - z) / a))
    else
        tmp = t / ((a - z) / (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 (z <= -8.8e+147) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 1.3e+101) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.8e+147:
		tmp = t * ((y - z) / (a - z))
	elif z <= 1.3e+101:
		tmp = x + ((t - x) * ((y - z) / a))
	else:
		tmp = t / ((a - z) / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.8e+147)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 1.3e+101)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)));
	else
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.8e+147)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 1.3e+101)
		tmp = x + ((t - x) * ((y - z) / a));
	else
		tmp = t / ((a - z) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.8e+147], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+101], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.8000000000000007e147

   1. Initial program 34.5%

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

      1. associate-/l* 54.0%

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

   3. Simplified 54.0%

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

   5. Taylor expanded in x around 0 39.9%

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

      1. associate-/l* 74.5%

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

   7. Simplified 74.5%

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

   if -8.8000000000000007e147 < z < 1.3e101

   1. Initial program 80.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 a around inf 67.7%

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

      1. associate-/l* 77.3%

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

   7. Simplified 77.3%

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

   if 1.3e101 < z

   1. Initial program 32.9%

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

      1. associate-/l* 64.2%

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

   3. Simplified 64.2%

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

   5. Taylor expanded in x around 0 36.8%

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

      1. associate-/l* 69.0%

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

      2. *-un-lft-identity 69.0%

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

      3. clear-num 69.0%

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

      4. div-inv 69.1%

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

   7. Applied egg-rr 69.1%

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

      1. *-un-lft-identity 69.1%

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

   9. Applied egg-rr 69.1%

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

Alternative 8: 34.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -15500:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-126}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+133}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -15500.0)
   t
   (if (<= z -5.7e-126) x (if (<= z 1.85e+133) (* t (/ y a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -15500.0) {
		tmp = t;
	} else if (z <= -5.7e-126) {
		tmp = x;
	} else if (z <= 1.85e+133) {
		tmp = t * (y / a);
	} 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 <= (-15500.0d0)) then
        tmp = t
    else if (z <= (-5.7d-126)) then
        tmp = x
    else if (z <= 1.85d+133) then
        tmp = t * (y / a)
    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 <= -15500.0) {
		tmp = t;
	} else if (z <= -5.7e-126) {
		tmp = x;
	} else if (z <= 1.85e+133) {
		tmp = t * (y / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -15500.0:
		tmp = t
	elif z <= -5.7e-126:
		tmp = x
	elif z <= 1.85e+133:
		tmp = t * (y / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -15500.0)
		tmp = t;
	elseif (z <= -5.7e-126)
		tmp = x;
	elseif (z <= 1.85e+133)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -15500.0)
		tmp = t;
	elseif (z <= -5.7e-126)
		tmp = x;
	elseif (z <= 1.85e+133)
		tmp = t * (y / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -15500.0], t, If[LessEqual[z, -5.7e-126], x, If[LessEqual[z, 1.85e+133], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -15500 or 1.85000000000000012e133 < z

   1. Initial program 39.0%

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

      1. associate-/l* 64.5%

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

   3. Simplified 64.5%

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

   5. Taylor expanded in z around inf 43.2%

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

   if -15500 < z < -5.69999999999999979e-126

   1. Initial program 78.8%

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

      1. associate-/l* 87.2%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in a around inf 54.1%

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

   if -5.69999999999999979e-126 < z < 1.85000000000000012e133

   1. Initial program 85.9%

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

      1. associate-/l* 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in x around 0 47.5%

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

   6. Taylor expanded in z around 0 31.4%

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

      1. associate-/l* 37.8%

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

   8. Simplified 37.8%

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

Alternative 9: 65.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3000 \lor \neg \left(z \leq 1.1 \cdot 10^{-101}\right):\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3000.0) (not (<= z 1.1e-101)))
   (/ t (/ (- a z) (- y z)))
   (+ x (/ (- t x) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3000.0) || !(z <= 1.1e-101)) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3000.0d0)) .or. (.not. (z <= 1.1d-101))) then
        tmp = t / ((a - z) / (y - z))
    else
        tmp = x + ((t - x) / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3000.0) || !(z <= 1.1e-101)) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3000.0) or not (z <= 1.1e-101):
		tmp = t / ((a - z) / (y - z))
	else:
		tmp = x + ((t - x) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3000.0) || !(z <= 1.1e-101))
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3000.0) || ~((z <= 1.1e-101)))
		tmp = t / ((a - z) / (y - z));
	else
		tmp = x + ((t - x) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3000.0], N[Not[LessEqual[z, 1.1e-101]], $MachinePrecision]], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3e3 or 1.0999999999999999e-101 < z

   1. Initial program 48.8%

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

      1. associate-/l* 71.3%

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

   3. Simplified 71.3%

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

   5. Taylor expanded in x around 0 38.0%

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

      1. associate-/l* 62.8%

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

      2. *-un-lft-identity 62.8%

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

      3. clear-num 62.7%

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

      4. div-inv 62.8%

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

   7. Applied egg-rr 62.8%

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

      1. *-un-lft-identity 62.8%

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

   9. Applied egg-rr 62.8%

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

   if -3e3 < z < 1.0999999999999999e-101

   1. Initial program 88.2%

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

      1. associate-/l* 88.3%

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

   3. Simplified 88.3%

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

      1. *-commutative 88.3%

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

      2. associate-*l/ 88.2%

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

      3. associate-*r/ 94.8%

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

      4. clear-num 93.9%

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

      5. un-div-inv 94.0%

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

   6. Applied egg-rr 94.0%

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

   7. Taylor expanded in z around 0 83.9%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3000 \lor \neg \left(z \leq 1.1 \cdot 10^{-101}\right):\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-24} \lor \neg \left(z \leq 2.1 \cdot 10^{-96}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.6e-24) (not (<= z 2.1e-96)))
   (* t (/ (- y z) (- a z)))
   (+ x (/ (- t x) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e-24) || !(z <= 2.1e-96)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.6d-24)) .or. (.not. (z <= 2.1d-96))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + ((t - x) / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e-24) || !(z <= 2.1e-96)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.6e-24) or not (z <= 2.1e-96):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + ((t - x) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.6e-24) || !(z <= 2.1e-96))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.6e-24) || ~((z <= 2.1e-96)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + ((t - x) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.6e-24], N[Not[LessEqual[z, 2.1e-96]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6e-24 or 2.10000000000000001e-96 < z

   1. Initial program 48.9%

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

      1. associate-/l* 70.8%

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

   3. Simplified 70.8%

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

   5. Taylor expanded in x around 0 37.7%

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

      1. associate-/l* 61.9%

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

   7. Simplified 61.9%

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

   if -2.6e-24 < z < 2.10000000000000001e-96

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l/ 89.8%

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

      3. associate-*r/ 96.6%

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

      4. clear-num 95.7%

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

      5. un-div-inv 95.8%

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

   6. Applied egg-rr 95.8%

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

   7. Taylor expanded in z around 0 86.3%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-24} \lor \neg \left(z \leq 2.1 \cdot 10^{-96}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+63} \lor \neg \left(z \leq 3.6 \cdot 10^{-113}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.5e+63) (not (<= z 3.6e-113)))
   (* t (/ (- y z) (- a z)))
   (+ x (* y (/ (- t x) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.5e+63) || !(z <= 3.6e-113)) {
		tmp = t * ((y - z) / (a - 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 ((z <= (-4.5d+63)) .or. (.not. (z <= 3.6d-113))) then
        tmp = t * ((y - z) / (a - 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 ((z <= -4.5e+63) || !(z <= 3.6e-113)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y * ((t - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.5e+63) or not (z <= 3.6e-113):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (y * ((t - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.5e+63) || !(z <= 3.6e-113))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - 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 ((z <= -4.5e+63) || ~((z <= 3.6e-113)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (y * ((t - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.5e+63], N[Not[LessEqual[z, 3.6e-113]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.50000000000000017e63 or 3.59999999999999975e-113 < z

   1. Initial program 47.0%

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

      1. associate-/l* 69.3%

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

   3. Simplified 69.3%

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

   5. Taylor expanded in x around 0 37.9%

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

      1. associate-/l* 63.9%

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

   7. Simplified 63.9%

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

   if -4.50000000000000017e63 < z < 3.59999999999999975e-113

   1. Initial program 86.6%

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

      1. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in z around 0 74.2%

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

      1. associate-/l* 77.1%

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

   7. Simplified 77.1%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+63} \lor \neg \left(z \leq 3.6 \cdot 10^{-113}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+79} \lor \neg \left(y \leq 1.05 \cdot 10^{+166}\right):\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -8.2e+79) (not (<= y 1.05e+166)))
   (* y (/ (- t x) (- a z)))
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -8.2e+79) || !(y <= 1.05e+166)) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t * ((y - z) / (a - 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 ((y <= (-8.2d+79)) .or. (.not. (y <= 1.05d+166))) then
        tmp = y * ((t - x) / (a - z))
    else
        tmp = t * ((y - z) / (a - 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 ((y <= -8.2e+79) || !(y <= 1.05e+166)) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -8.2e+79) or not (y <= 1.05e+166):
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -8.2e+79) || !(y <= 1.05e+166))
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -8.2e+79) || ~((y <= 1.05e+166)))
		tmp = y * ((t - x) / (a - z));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -8.2e+79], N[Not[LessEqual[y, 1.05e+166]], $MachinePrecision]], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.2e79 or 1.05e166 < y

   1. Initial program 60.4%

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

      1. associate-/l* 85.0%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in y around inf 82.9%

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

      1. div-sub 82.9%

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

   7. Simplified 82.9%

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

   if -8.2e79 < y < 1.05e166

   1. Initial program 66.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 x around 0 42.8%

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

      1. associate-/l* 59.1%

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

   7. Simplified 59.1%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+79} \lor \neg \left(y \leq 1.05 \cdot 10^{+166}\right):\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+121}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.55e+103)
   (* x (- 1.0 (/ y a)))
   (if (<= x 3.3e+121) (* t (/ (- y z) (- a z))) (* (- y a) (/ x z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.55e+103) {
		tmp = x * (1.0 - (y / a));
	} else if (x <= 3.3e+121) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = (y - a) * (x / 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 (x <= (-1.55d+103)) then
        tmp = x * (1.0d0 - (y / a))
    else if (x <= 3.3d+121) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = (y - a) * (x / 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 (x <= -1.55e+103) {
		tmp = x * (1.0 - (y / a));
	} else if (x <= 3.3e+121) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = (y - a) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.55e+103:
		tmp = x * (1.0 - (y / a))
	elif x <= 3.3e+121:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = (y - a) * (x / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.55e+103)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (x <= 3.3e+121)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(Float64(y - a) * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.55e+103)
		tmp = x * (1.0 - (y / a));
	elseif (x <= 3.3e+121)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = (y - a) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.55e+103], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e+121], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.5500000000000001e103

   1. Initial program 61.9%

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

      1. associate-/l* 78.0%

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

   3. Simplified 78.0%

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

      1. *-commutative 78.0%

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

      2. associate-*l/ 61.9%

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

      3. associate-*r/ 80.7%

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

      4. clear-num 80.7%

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

      5. un-div-inv 80.7%

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

   6. Applied egg-rr 80.7%

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

   7. Taylor expanded in z around 0 64.0%

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

   8. Taylor expanded in x around inf 61.0%

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

      1. mul-1-neg 61.0%

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

      2. unsub-neg 61.0%

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

   10. Simplified 61.0%

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

   if -1.5500000000000001e103 < x < 3.29999999999999979e121

   1. Initial program 70.0%

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

      1. associate-/l* 81.8%

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

   3. Simplified 81.8%

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

   5. Taylor expanded in x around 0 53.8%

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

      1. associate-/l* 72.8%

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

   7. Simplified 72.8%

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

   if 3.29999999999999979e121 < x

   1. Initial program 41.9%

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

      1. associate-/l* 61.5%

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

   3. Simplified 61.5%

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

   5. Taylor expanded in x around -inf 65.0%

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

      1. associate-*r* 65.0%

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

      2. neg-mul-1 65.0%

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

   7. Simplified 65.0%

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

   8. Taylor expanded in z around -inf 33.3%

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

      1. associate-/l* 46.7%

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

   10. Applied egg-rr 46.7%

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

       1. associate-*r/ 33.3%

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

       2. *-commutative 33.3%

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

       3. associate-*r/ 46.7%

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

       4. *-commutative 46.7%

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

   12. Simplified 46.7%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+121}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 35.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+147}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+133}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.8e+147) t (if (<= z 7e+133) (* t (/ (- y z) a)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e+147) {
		tmp = t;
	} else if (z <= 7e+133) {
		tmp = t * ((y - z) / a);
	} 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 <= (-8.8d+147)) then
        tmp = t
    else if (z <= 7d+133) then
        tmp = t * ((y - z) / a)
    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 <= -8.8e+147) {
		tmp = t;
	} else if (z <= 7e+133) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.8e+147:
		tmp = t
	elif z <= 7e+133:
		tmp = t * ((y - z) / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.8e+147)
		tmp = t;
	elseif (z <= 7e+133)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.8e+147)
		tmp = t;
	elseif (z <= 7e+133)
		tmp = t * ((y - z) / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.8e+147], t, If[LessEqual[z, 7e+133], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -8.8000000000000007e147 or 6.9999999999999997e133 < z

   1. Initial program 31.5%

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

      1. associate-/l* 57.9%

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

   3. Simplified 57.9%

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

   5. Taylor expanded in z around inf 51.0%

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

   if -8.8000000000000007e147 < z < 6.9999999999999997e133

   1. Initial program 80.2%

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

      1. associate-/l* 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in x around 0 43.0%

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

   6. Taylor expanded in a around inf 33.3%

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

      1. associate-/l* 39.9%

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

   8. Simplified 39.9%

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

Alternative 15: 38.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2200:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2200.0) t (if (<= z 8.2e-36) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2200.0) {
		tmp = t;
	} else if (z <= 8.2e-36) {
		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 <= (-2200.0d0)) then
        tmp = t
    else if (z <= 8.2d-36) 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 <= -2200.0) {
		tmp = t;
	} else if (z <= 8.2e-36) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2200.0:
		tmp = t
	elif z <= 8.2e-36:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2200.0)
		tmp = t;
	elseif (z <= 8.2e-36)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2200.0)
		tmp = t;
	elseif (z <= 8.2e-36)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2200.0], t, If[LessEqual[z, 8.2e-36], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -2200 or 8.20000000000000025e-36 < z

   1. Initial program 44.5%

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

      1. associate-/l* 68.5%

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

   3. Simplified 68.5%

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

   5. Taylor expanded in z around inf 38.5%

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

   if -2200 < z < 8.20000000000000025e-36

   1. Initial program 88.7%

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

      1. associate-/l* 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in a around inf 34.7%

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

Alternative 16: 25.6% 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 64.2%

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

   1. associate-/l* 77.9%

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

3. Simplified 77.9%

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

5. Taylor expanded in z around inf 23.8%

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

Developer Target 1: 83.5% 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 2024116 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

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

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