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

Percentage Accurate: 69.3% → 91.1%

Time: 14.0s

Alternatives: 16

Speedup: 0.7×

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: 69.3% 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: 91.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-274} \lor \neg \left(t\_1 \leq 10^{-282}\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -1e-274) (not (<= t_1 1e-282)))
     (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 <= -1e-274) || !(t_1 <= 1e-282)) {
		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 <= -1e-274) || !(t_1 <= 1e-282))
		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, -1e-274], N[Not[LessEqual[t$95$1, 1e-282]], $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))) < -9.99999999999999966e-275 or 1e-282 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 72.4%

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

      1. +-commutative 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-/l* 89.4%

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

      4. fma-define 89.5%

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

   3. Simplified 89.5%

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

   if -9.99999999999999966e-275 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 1e-282

   1. Initial program 5.7%

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

      1. associate-/l* 4.9%

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

   3. Simplified 4.9%

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

   5. Taylor expanded in z around inf 99.4%

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

      1. associate--l+ 99.4%

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

      2. associate-*r/ 99.4%

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

      3. associate-*r/ 99.4%

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

      4. mul-1-neg 99.4%

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

      5. div-sub 99.3%

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

      6. mul-1-neg 99.3%

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

      7. distribute-lft-out-- 99.3%

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

      8. associate-*r/ 99.3%

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

      9. mul-1-neg 99.3%

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

      10. unsub-neg 99.3%

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

      11. distribute-rgt-out-- 99.4%

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

   7. Simplified 99.4%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-274} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 10^{-282}\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-282}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -5e-163)
     t_1
     (if (<= t_2 1e-282)
       (+ t (/ (* (- t x) (- a y)) z))
       (if (<= t_2 5e+304) 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 <= -5e-163) {
		tmp = t_1;
	} else if (t_2 <= 1e-282) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 5e+304) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    t_2 = x + (((y - z) * (t - x)) / (a - z))
    if (t_2 <= (-5d-163)) then
        tmp = t_1
    else if (t_2 <= 1d-282) then
        tmp = t + (((t - x) * (a - y)) / z)
    else if (t_2 <= 5d+304) then
        tmp = t_2
    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 - z) * ((t - x) / (a - z)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -5e-163) {
		tmp = t_1;
	} else if (t_2 <= 1e-282) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 5e+304) {
		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 <= -5e-163:
		tmp = t_1
	elif t_2 <= 1e-282:
		tmp = t + (((t - x) * (a - y)) / z)
	elif t_2 <= 5e+304:
		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 <= -5e-163)
		tmp = t_1;
	elseif (t_2 <= 1e-282)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (t_2 <= 5e+304)
		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 <= -5e-163)
		tmp = t_1;
	elseif (t_2 <= 1e-282)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (t_2 <= 5e+304)
		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, -5e-163], t$95$1, If[LessEqual[t$95$2, 1e-282], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+304], 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))) < -4.99999999999999977e-163 or 4.9999999999999997e304 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 61.4%

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

      1. associate-/l* 86.2%

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

   3. Simplified 86.2%

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

   if -4.99999999999999977e-163 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 1e-282

   1. Initial program 19.5%

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

      1. associate-/l* 13.0%

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

   3. Simplified 13.0%

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

   5. Taylor expanded in z around inf 95.6%

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

      1. associate--l+ 95.6%

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

      2. associate-*r/ 95.6%

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

      3. associate-*r/ 95.6%

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

      4. mul-1-neg 95.6%

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

      5. div-sub 95.5%

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

      6. mul-1-neg 95.5%

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

      7. distribute-lft-out-- 95.5%

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

      8. associate-*r/ 95.5%

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

      9. mul-1-neg 95.5%

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

      10. unsub-neg 95.5%

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

      11. distribute-rgt-out-- 95.6%

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

   7. Simplified 95.6%

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

   if 1e-282 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 4.9999999999999997e304

   1. Initial program 97.0%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -5 \cdot 10^{-163}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 10^{-282}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 38.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+71}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-239}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-112}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= z -4.5e+71)
     t
     (if (<= z -1.9e-56)
       x
       (if (<= z -8.5e-239)
         t_1
         (if (<= z 1.32e-112) x (if (<= z 1.22e+84) t_1 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (z <= -4.5e+71) {
		tmp = t;
	} else if (z <= -1.9e-56) {
		tmp = x;
	} else if (z <= -8.5e-239) {
		tmp = t_1;
	} else if (z <= 1.32e-112) {
		tmp = x;
	} else if (z <= 1.22e+84) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (a - z))
    if (z <= (-4.5d+71)) then
        tmp = t
    else if (z <= (-1.9d-56)) then
        tmp = x
    else if (z <= (-8.5d-239)) then
        tmp = t_1
    else if (z <= 1.32d-112) then
        tmp = x
    else if (z <= 1.22d+84) then
        tmp = t_1
    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 t_1 = t * (y / (a - z));
	double tmp;
	if (z <= -4.5e+71) {
		tmp = t;
	} else if (z <= -1.9e-56) {
		tmp = x;
	} else if (z <= -8.5e-239) {
		tmp = t_1;
	} else if (z <= 1.32e-112) {
		tmp = x;
	} else if (z <= 1.22e+84) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if z <= -4.5e+71:
		tmp = t
	elif z <= -1.9e-56:
		tmp = x
	elif z <= -8.5e-239:
		tmp = t_1
	elif z <= 1.32e-112:
		tmp = x
	elif z <= 1.22e+84:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (z <= -4.5e+71)
		tmp = t;
	elseif (z <= -1.9e-56)
		tmp = x;
	elseif (z <= -8.5e-239)
		tmp = t_1;
	elseif (z <= 1.32e-112)
		tmp = x;
	elseif (z <= 1.22e+84)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (z <= -4.5e+71)
		tmp = t;
	elseif (z <= -1.9e-56)
		tmp = x;
	elseif (z <= -8.5e-239)
		tmp = t_1;
	elseif (z <= 1.32e-112)
		tmp = x;
	elseif (z <= 1.22e+84)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+71], t, If[LessEqual[z, -1.9e-56], x, If[LessEqual[z, -8.5e-239], t$95$1, If[LessEqual[z, 1.32e-112], x, If[LessEqual[z, 1.22e+84], t$95$1, t]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.50000000000000043e71 or 1.2200000000000001e84 < z

   1. Initial program 35.9%

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

      1. associate-/l* 59.9%

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

   3. Simplified 59.9%

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

   5. Taylor expanded in z around inf 47.8%

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

   if -4.50000000000000043e71 < z < -1.9000000000000001e-56 or -8.49999999999999958e-239 < z < 1.32000000000000008e-112

   1. Initial program 88.1%

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

      1. associate-/l* 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in a around inf 45.2%

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

   if -1.9000000000000001e-56 < z < -8.49999999999999958e-239 or 1.32000000000000008e-112 < z < 1.2200000000000001e84

   1. Initial program 87.5%

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

      1. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in y around inf 63.9%

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

      1. div-sub 66.3%

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

   7. Simplified 66.3%

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

   8. Taylor expanded in t around inf 38.1%

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

      1. associate-/l* 46.1%

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

   10. Simplified 46.1%

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

Alternative 4: 37.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+71}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-239}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-111}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 85000000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= z -6.5e+71)
     t
     (if (<= z -1.85e-58)
       x
       (if (<= z -1.1e-239)
         t_1
         (if (<= z 5e-111)
           x
           (if (<= z 1.3e-28) t_1 (if (<= z 85000000000000.0) x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -6.5e+71) {
		tmp = t;
	} else if (z <= -1.85e-58) {
		tmp = x;
	} else if (z <= -1.1e-239) {
		tmp = t_1;
	} else if (z <= 5e-111) {
		tmp = x;
	} else if (z <= 1.3e-28) {
		tmp = t_1;
	} else if (z <= 85000000000000.0) {
		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) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (z <= (-6.5d+71)) then
        tmp = t
    else if (z <= (-1.85d-58)) then
        tmp = x
    else if (z <= (-1.1d-239)) then
        tmp = t_1
    else if (z <= 5d-111) then
        tmp = x
    else if (z <= 1.3d-28) then
        tmp = t_1
    else if (z <= 85000000000000.0d0) 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 t_1 = t * (y / a);
	double tmp;
	if (z <= -6.5e+71) {
		tmp = t;
	} else if (z <= -1.85e-58) {
		tmp = x;
	} else if (z <= -1.1e-239) {
		tmp = t_1;
	} else if (z <= 5e-111) {
		tmp = x;
	} else if (z <= 1.3e-28) {
		tmp = t_1;
	} else if (z <= 85000000000000.0) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if z <= -6.5e+71:
		tmp = t
	elif z <= -1.85e-58:
		tmp = x
	elif z <= -1.1e-239:
		tmp = t_1
	elif z <= 5e-111:
		tmp = x
	elif z <= 1.3e-28:
		tmp = t_1
	elif z <= 85000000000000.0:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (z <= -6.5e+71)
		tmp = t;
	elseif (z <= -1.85e-58)
		tmp = x;
	elseif (z <= -1.1e-239)
		tmp = t_1;
	elseif (z <= 5e-111)
		tmp = x;
	elseif (z <= 1.3e-28)
		tmp = t_1;
	elseif (z <= 85000000000000.0)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (z <= -6.5e+71)
		tmp = t;
	elseif (z <= -1.85e-58)
		tmp = x;
	elseif (z <= -1.1e-239)
		tmp = t_1;
	elseif (z <= 5e-111)
		tmp = x;
	elseif (z <= 1.3e-28)
		tmp = t_1;
	elseif (z <= 85000000000000.0)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+71], t, If[LessEqual[z, -1.85e-58], x, If[LessEqual[z, -1.1e-239], t$95$1, If[LessEqual[z, 5e-111], x, If[LessEqual[z, 1.3e-28], t$95$1, If[LessEqual[z, 85000000000000.0], x, t]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.49999999999999954e71 or 8.5e13 < z

   1. Initial program 39.5%

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

      1. associate-/l* 64.0%

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

   3. Simplified 64.0%

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

   5. Taylor expanded in z around inf 45.3%

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

   if -6.49999999999999954e71 < z < -1.8500000000000001e-58 or -1.09999999999999991e-239 < z < 5.0000000000000003e-111 or 1.3e-28 < z < 8.5e13

   1. Initial program 88.9%

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

      1. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in a around inf 46.2%

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

   if -1.8500000000000001e-58 < z < -1.09999999999999991e-239 or 5.0000000000000003e-111 < z < 1.3e-28

   1. Initial program 93.8%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in y around inf 68.3%

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

      1. div-sub 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in a around inf 54.6%

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

   9. Taylor expanded in t around inf 34.2%

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

       1. associate-/l* 45.4%

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

   11. Simplified 45.4%

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

Alternative 5: 37.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-239}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+72)
   t
   (if (<= z -2.9e-66)
     x
     (if (<= z -5.8e-239)
       (* t (/ y a))
       (if (<= z 4.2e-61) x (if (<= z 4e+45) (* t (/ y (- z))) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+72) {
		tmp = t;
	} else if (z <= -2.9e-66) {
		tmp = x;
	} else if (z <= -5.8e-239) {
		tmp = t * (y / a);
	} else if (z <= 4.2e-61) {
		tmp = x;
	} else if (z <= 4e+45) {
		tmp = t * (y / -z);
	} 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 <= (-1.05d+72)) then
        tmp = t
    else if (z <= (-2.9d-66)) then
        tmp = x
    else if (z <= (-5.8d-239)) then
        tmp = t * (y / a)
    else if (z <= 4.2d-61) then
        tmp = x
    else if (z <= 4d+45) then
        tmp = t * (y / -z)
    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 <= -1.05e+72) {
		tmp = t;
	} else if (z <= -2.9e-66) {
		tmp = x;
	} else if (z <= -5.8e-239) {
		tmp = t * (y / a);
	} else if (z <= 4.2e-61) {
		tmp = x;
	} else if (z <= 4e+45) {
		tmp = t * (y / -z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.05e+72:
		tmp = t
	elif z <= -2.9e-66:
		tmp = x
	elif z <= -5.8e-239:
		tmp = t * (y / a)
	elif z <= 4.2e-61:
		tmp = x
	elif z <= 4e+45:
		tmp = t * (y / -z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+72)
		tmp = t;
	elseif (z <= -2.9e-66)
		tmp = x;
	elseif (z <= -5.8e-239)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 4.2e-61)
		tmp = x;
	elseif (z <= 4e+45)
		tmp = Float64(t * Float64(y / Float64(-z)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.05e+72)
		tmp = t;
	elseif (z <= -2.9e-66)
		tmp = x;
	elseif (z <= -5.8e-239)
		tmp = t * (y / a);
	elseif (z <= 4.2e-61)
		tmp = x;
	elseif (z <= 4e+45)
		tmp = t * (y / -z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+72], t, If[LessEqual[z, -2.9e-66], x, If[LessEqual[z, -5.8e-239], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-61], x, If[LessEqual[z, 4e+45], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.0500000000000001e72 or 3.9999999999999997e45 < 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* 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 z around inf 46.7%

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

   if -1.0500000000000001e72 < z < -2.90000000000000011e-66 or -5.8000000000000004e-239 < z < 4.1999999999999998e-61

   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* 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in a around inf 42.7%

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

   if -2.90000000000000011e-66 < z < -5.8000000000000004e-239

   1. Initial program 93.3%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in y around inf 68.0%

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

      1. div-sub 72.7%

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

   7. Simplified 72.7%

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

   8. Taylor expanded in a around inf 58.3%

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

   9. Taylor expanded in t around inf 35.5%

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

       1. associate-/l* 46.6%

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

   11. Simplified 46.6%

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

   if 4.1999999999999998e-61 < z < 3.9999999999999997e45

   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* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in x around 0 61.8%

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

      1. associate-/l* 71.0%

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

   7. Simplified 71.0%

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

   8. Taylor expanded in a around 0 62.4%

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

      1. associate-*r/ 62.4%

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

      2. neg-mul-1 62.4%

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

   10. Simplified 62.4%

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

   11. Taylor expanded in y around inf 45.0%

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

       1. mul-1-neg 45.0%

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

       2. associate-/l* 49.5%

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

       3. distribute-lft-neg-in 49.5%

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

   13. Simplified 49.5%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-239}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -6.7 \cdot 10^{+37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \left(\frac{z}{a - z} + 1\right)\\ \mathbf{elif}\;y \leq 155000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -6.7e+37)
     t_2
     (if (<= y -4.7e-83)
       t_1
       (if (<= y -3.5e-217)
         (* x (+ (/ z (- a z)) 1.0))
         (if (<= y 155000.0) 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 <= -6.7e+37) {
		tmp = t_2;
	} else if (y <= -4.7e-83) {
		tmp = t_1;
	} else if (y <= -3.5e-217) {
		tmp = x * ((z / (a - z)) + 1.0);
	} else if (y <= 155000.0) {
		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 <= (-6.7d+37)) then
        tmp = t_2
    else if (y <= (-4.7d-83)) then
        tmp = t_1
    else if (y <= (-3.5d-217)) then
        tmp = x * ((z / (a - z)) + 1.0d0)
    else if (y <= 155000.0d0) 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 <= -6.7e+37) {
		tmp = t_2;
	} else if (y <= -4.7e-83) {
		tmp = t_1;
	} else if (y <= -3.5e-217) {
		tmp = x * ((z / (a - z)) + 1.0);
	} else if (y <= 155000.0) {
		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 <= -6.7e+37:
		tmp = t_2
	elif y <= -4.7e-83:
		tmp = t_1
	elif y <= -3.5e-217:
		tmp = x * ((z / (a - z)) + 1.0)
	elif y <= 155000.0:
		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 <= -6.7e+37)
		tmp = t_2;
	elseif (y <= -4.7e-83)
		tmp = t_1;
	elseif (y <= -3.5e-217)
		tmp = Float64(x * Float64(Float64(z / Float64(a - z)) + 1.0));
	elseif (y <= 155000.0)
		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 <= -6.7e+37)
		tmp = t_2;
	elseif (y <= -4.7e-83)
		tmp = t_1;
	elseif (y <= -3.5e-217)
		tmp = x * ((z / (a - z)) + 1.0);
	elseif (y <= 155000.0)
		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, -6.7e+37], t$95$2, If[LessEqual[y, -4.7e-83], t$95$1, If[LessEqual[y, -3.5e-217], N[(x * N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 155000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.69999999999999968e37 or 155000 < y

   1. Initial program 69.0%

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

      1. associate-/l* 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in y around inf 75.9%

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

      1. div-sub 77.5%

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

   7. Simplified 77.5%

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

   if -6.69999999999999968e37 < y < -4.7000000000000003e-83 or -3.5e-217 < y < 155000

   1. Initial program 62.2%

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

      1. associate-/l* 72.2%

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

   3. Simplified 72.2%

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

   5. Taylor expanded in x around 0 42.9%

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

      1. associate-/l* 57.1%

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

   7. Simplified 57.1%

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

   if -4.7000000000000003e-83 < y < -3.5e-217

   1. Initial program 76.7%

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

      1. associate-/l* 77.2%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in x around -inf 57.3%

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

      1. mul-1-neg 57.3%

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

      2. *-commutative 57.3%

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

      3. distribute-rgt-neg-in 57.3%

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

   7. Simplified 57.3%

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

   8. Taylor expanded in y around 0 56.9%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.7 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \left(\frac{z}{a - z} + 1\right)\\ \mathbf{elif}\;y \leq 155000:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{-22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-211}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= t -6.2e-22)
     t_2
     (if (<= t -4.5e-169)
       t_1
       (if (<= t -2.4e-211)
         (+ t (* x (/ y z)))
         (if (<= t 3.4e-80) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -6.2e-22) {
		tmp = t_2;
	} else if (t <= -4.5e-169) {
		tmp = t_1;
	} else if (t <= -2.4e-211) {
		tmp = t + (x * (y / z));
	} else if (t <= 3.4e-80) {
		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 = x * (1.0d0 - (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (t <= (-6.2d-22)) then
        tmp = t_2
    else if (t <= (-4.5d-169)) then
        tmp = t_1
    else if (t <= (-2.4d-211)) then
        tmp = t + (x * (y / z))
    else if (t <= 3.4d-80) 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 = x * (1.0 - (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -6.2e-22) {
		tmp = t_2;
	} else if (t <= -4.5e-169) {
		tmp = t_1;
	} else if (t <= -2.4e-211) {
		tmp = t + (x * (y / z));
	} else if (t <= 3.4e-80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -6.2e-22:
		tmp = t_2
	elif t <= -4.5e-169:
		tmp = t_1
	elif t <= -2.4e-211:
		tmp = t + (x * (y / z))
	elif t <= 3.4e-80:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -6.2e-22)
		tmp = t_2;
	elseif (t <= -4.5e-169)
		tmp = t_1;
	elseif (t <= -2.4e-211)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	elseif (t <= 3.4e-80)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -6.2e-22)
		tmp = t_2;
	elseif (t <= -4.5e-169)
		tmp = t_1;
	elseif (t <= -2.4e-211)
		tmp = t + (x * (y / z));
	elseif (t <= 3.4e-80)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.2e-22], t$95$2, If[LessEqual[t, -4.5e-169], t$95$1, If[LessEqual[t, -2.4e-211], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e-80], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.20000000000000025e-22 or 3.4000000000000001e-80 < t

   1. Initial program 62.5%

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

      1. associate-/l* 85.5%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in x around 0 51.0%

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

      1. associate-/l* 72.1%

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

   7. Simplified 72.1%

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

   if -6.20000000000000025e-22 < t < -4.4999999999999999e-169 or -2.4000000000000002e-211 < t < 3.4000000000000001e-80

   1. Initial program 76.0%

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

      1. associate-/l* 74.1%

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

   3. Simplified 74.1%

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

   5. Taylor expanded in x around -inf 68.5%

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

      1. mul-1-neg 68.5%

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

      2. *-commutative 68.5%

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

      3. distribute-rgt-neg-in 68.5%

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

   7. Simplified 68.5%

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

   8. Taylor expanded in z around 0 55.1%

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

      1. mul-1-neg 55.1%

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

      2. sub-neg 55.1%

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

      3. metadata-eval 55.1%

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

   10. Simplified 55.1%

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

   if -4.4999999999999999e-169 < t < -2.4000000000000002e-211

   1. Initial program 37.1%

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

      1. associate-/l* 46.7%

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

   3. Simplified 46.7%

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

   5. Taylor expanded in z around inf 90.8%

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

      1. associate--l+ 90.8%

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

      2. associate-*r/ 90.8%

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

      3. associate-*r/ 90.8%

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

      4. mul-1-neg 90.8%

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

      5. div-sub 90.8%

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

      6. mul-1-neg 90.8%

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

      7. distribute-lft-out-- 90.8%

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

      8. associate-*r/ 90.8%

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

      9. mul-1-neg 90.8%

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

      10. unsub-neg 90.8%

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

      11. distribute-rgt-out-- 90.8%

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

   7. Simplified 90.8%

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

   8. Taylor expanded in y around inf 86.2%

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

   9. Taylor expanded in t around 0 86.2%

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

       1. mul-1-neg 86.2%

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

       2. associate-/l* 89.5%

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

       3. distribute-rgt-neg-in 89.5%

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

       4. distribute-neg-frac2 89.5%

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

   11. Simplified 89.5%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-22}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-169}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-211}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -2.9 \cdot 10^{+38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-300}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) z))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -2.9e+38)
     t_2
     (if (<= a -2.6e-172)
       t_1
       (if (<= a -5e-300) (+ t (* x (/ y z))) (if (<= a 2.95e-31) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -2.9e+38) {
		tmp = t_2;
	} else if (a <= -2.6e-172) {
		tmp = t_1;
	} else if (a <= -5e-300) {
		tmp = t + (x * (y / z));
	} else if (a <= 2.95e-31) {
		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 * ((z - y) / z)
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-2.9d+38)) then
        tmp = t_2
    else if (a <= (-2.6d-172)) then
        tmp = t_1
    else if (a <= (-5d-300)) then
        tmp = t + (x * (y / z))
    else if (a <= 2.95d-31) 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 * ((z - y) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -2.9e+38) {
		tmp = t_2;
	} else if (a <= -2.6e-172) {
		tmp = t_1;
	} else if (a <= -5e-300) {
		tmp = t + (x * (y / z));
	} else if (a <= 2.95e-31) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / z)
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -2.9e+38:
		tmp = t_2
	elif a <= -2.6e-172:
		tmp = t_1
	elif a <= -5e-300:
		tmp = t + (x * (y / z))
	elif a <= 2.95e-31:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / z))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -2.9e+38)
		tmp = t_2;
	elseif (a <= -2.6e-172)
		tmp = t_1;
	elseif (a <= -5e-300)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	elseif (a <= 2.95e-31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / z);
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -2.9e+38)
		tmp = t_2;
	elseif (a <= -2.6e-172)
		tmp = t_1;
	elseif (a <= -5e-300)
		tmp = t + (x * (y / z));
	elseif (a <= 2.95e-31)
		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[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.9e+38], t$95$2, If[LessEqual[a, -2.6e-172], t$95$1, If[LessEqual[a, -5e-300], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.95e-31], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.90000000000000007e38 or 2.95000000000000016e-31 < a

   1. Initial program 64.0%

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

      1. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in x around -inf 58.7%

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

      1. mul-1-neg 58.7%

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

      2. *-commutative 58.7%

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

      3. distribute-rgt-neg-in 58.7%

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

   7. Simplified 58.7%

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

   8. Taylor expanded in z around 0 50.3%

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

      1. mul-1-neg 50.3%

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

      2. sub-neg 50.3%

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

      3. metadata-eval 50.3%

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

   10. Simplified 50.3%

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

   if -2.90000000000000007e38 < a < -2.5999999999999998e-172 or -4.99999999999999996e-300 < a < 2.95000000000000016e-31

   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* 74.2%

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

   3. Simplified 74.2%

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

   5. Taylor expanded in x around 0 60.9%

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

      1. associate-/l* 74.6%

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

   7. Simplified 74.6%

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

   8. Taylor expanded in a around 0 66.8%

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

      1. associate-*r/ 66.8%

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

      2. neg-mul-1 66.8%

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

   10. Simplified 66.8%

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

   11. Taylor expanded in t around 0 53.2%

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

       1. associate-/l* 66.8%

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

   13. Simplified 66.8%

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

   if -2.5999999999999998e-172 < a < -4.99999999999999996e-300

   1. Initial program 74.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 89.5%

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

      1. associate--l+ 89.5%

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

      2. associate-*r/ 89.5%

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

      3. associate-*r/ 89.5%

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

      4. mul-1-neg 89.5%

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

      5. div-sub 89.5%

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

      6. mul-1-neg 89.5%

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

      7. distribute-lft-out-- 89.5%

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

      8. associate-*r/ 89.5%

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

      9. mul-1-neg 89.5%

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

      10. unsub-neg 89.5%

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

      11. distribute-rgt-out-- 89.5%

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

   7. Simplified 89.5%

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

   8. Taylor expanded in y around inf 89.5%

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

   9. Taylor expanded in t around 0 67.7%

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

       1. mul-1-neg 67.7%

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

       2. associate-/l* 70.3%

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

       3. distribute-rgt-neg-in 70.3%

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

       4. distribute-neg-frac2 70.3%

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

   11. Simplified 70.3%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-172}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-300}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{-31}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -4.7 \cdot 10^{+38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-299}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) z))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -4.7e+38)
     t_2
     (if (<= a -1.4e-176)
       t_1
       (if (<= a -6.5e-299)
         (* y (/ (- x t) z))
         (if (<= a 1.25e-31) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -4.7e+38) {
		tmp = t_2;
	} else if (a <= -1.4e-176) {
		tmp = t_1;
	} else if (a <= -6.5e-299) {
		tmp = y * ((x - t) / z);
	} else if (a <= 1.25e-31) {
		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 * ((z - y) / z)
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-4.7d+38)) then
        tmp = t_2
    else if (a <= (-1.4d-176)) then
        tmp = t_1
    else if (a <= (-6.5d-299)) then
        tmp = y * ((x - t) / z)
    else if (a <= 1.25d-31) 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 * ((z - y) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -4.7e+38) {
		tmp = t_2;
	} else if (a <= -1.4e-176) {
		tmp = t_1;
	} else if (a <= -6.5e-299) {
		tmp = y * ((x - t) / z);
	} else if (a <= 1.25e-31) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / z)
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -4.7e+38:
		tmp = t_2
	elif a <= -1.4e-176:
		tmp = t_1
	elif a <= -6.5e-299:
		tmp = y * ((x - t) / z)
	elif a <= 1.25e-31:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / z))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -4.7e+38)
		tmp = t_2;
	elseif (a <= -1.4e-176)
		tmp = t_1;
	elseif (a <= -6.5e-299)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (a <= 1.25e-31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / z);
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -4.7e+38)
		tmp = t_2;
	elseif (a <= -1.4e-176)
		tmp = t_1;
	elseif (a <= -6.5e-299)
		tmp = y * ((x - t) / z);
	elseif (a <= 1.25e-31)
		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[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.7e+38], t$95$2, If[LessEqual[a, -1.4e-176], t$95$1, If[LessEqual[a, -6.5e-299], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e-31], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.6999999999999999e38 or 1.25e-31 < a

   1. Initial program 64.0%

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

      1. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in x around -inf 58.7%

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

      1. mul-1-neg 58.7%

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

      2. *-commutative 58.7%

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

      3. distribute-rgt-neg-in 58.7%

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

   7. Simplified 58.7%

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

   8. Taylor expanded in z around 0 50.3%

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

      1. mul-1-neg 50.3%

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

      2. sub-neg 50.3%

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

      3. metadata-eval 50.3%

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

   10. Simplified 50.3%

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

   if -4.6999999999999999e38 < a < -1.4000000000000001e-176 or -6.4999999999999997e-299 < a < 1.25e-31

   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* 74.1%

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

   3. Simplified 74.1%

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

   5. Taylor expanded in x around 0 61.2%

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

      1. associate-/l* 74.8%

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

   7. Simplified 74.8%

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

   8. Taylor expanded in a around 0 67.1%

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

      1. associate-*r/ 67.1%

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

      2. neg-mul-1 67.1%

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

   10. Simplified 67.1%

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

   11. Taylor expanded in t around 0 53.6%

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

       1. associate-/l* 67.1%

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

   13. Simplified 67.1%

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

   if -1.4000000000000001e-176 < a < -6.4999999999999997e-299

   1. Initial program 75.0%

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

      1. associate-/l* 71.7%

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

   3. Simplified 71.7%

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

   5. Taylor expanded in y around inf 61.4%

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

      1. div-sub 65.1%

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

   7. Simplified 65.1%

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

   8. Taylor expanded in a around 0 61.2%

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

      1. mul-1-neg 61.2%

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

      2. distribute-neg-frac2 61.2%

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

   10. Simplified 61.2%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-176}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-299}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-31}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{+38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-259}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) z))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -4.5e+38)
     t_2
     (if (<= a -3.5e-178)
       t_1
       (if (<= a -3.2e-259) (* x (/ y z)) (if (<= a 1.05e-28) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -4.5e+38) {
		tmp = t_2;
	} else if (a <= -3.5e-178) {
		tmp = t_1;
	} else if (a <= -3.2e-259) {
		tmp = x * (y / z);
	} else if (a <= 1.05e-28) {
		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 * ((z - y) / z)
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-4.5d+38)) then
        tmp = t_2
    else if (a <= (-3.5d-178)) then
        tmp = t_1
    else if (a <= (-3.2d-259)) then
        tmp = x * (y / z)
    else if (a <= 1.05d-28) 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 * ((z - y) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -4.5e+38) {
		tmp = t_2;
	} else if (a <= -3.5e-178) {
		tmp = t_1;
	} else if (a <= -3.2e-259) {
		tmp = x * (y / z);
	} else if (a <= 1.05e-28) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / z)
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -4.5e+38:
		tmp = t_2
	elif a <= -3.5e-178:
		tmp = t_1
	elif a <= -3.2e-259:
		tmp = x * (y / z)
	elif a <= 1.05e-28:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / z))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -4.5e+38)
		tmp = t_2;
	elseif (a <= -3.5e-178)
		tmp = t_1;
	elseif (a <= -3.2e-259)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.05e-28)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / z);
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -4.5e+38)
		tmp = t_2;
	elseif (a <= -3.5e-178)
		tmp = t_1;
	elseif (a <= -3.2e-259)
		tmp = x * (y / z);
	elseif (a <= 1.05e-28)
		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[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.5e+38], t$95$2, If[LessEqual[a, -3.5e-178], t$95$1, If[LessEqual[a, -3.2e-259], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e-28], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.4999999999999998e38 or 1.05000000000000003e-28 < a

   1. Initial program 64.0%

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

      1. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in x around -inf 58.7%

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

      1. mul-1-neg 58.7%

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

      2. *-commutative 58.7%

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

      3. distribute-rgt-neg-in 58.7%

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

   7. Simplified 58.7%

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

   8. Taylor expanded in z around 0 50.3%

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

      1. mul-1-neg 50.3%

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

      2. sub-neg 50.3%

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

      3. metadata-eval 50.3%

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

   10. Simplified 50.3%

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

   if -4.4999999999999998e38 < a < -3.49999999999999983e-178 or -3.19999999999999988e-259 < a < 1.05000000000000003e-28

   1. Initial program 68.2%

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

      1. associate-/l* 72.9%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in x around 0 59.4%

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

      1. associate-/l* 72.2%

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

   7. Simplified 72.2%

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

   8. Taylor expanded in a around 0 65.3%

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

      1. associate-*r/ 65.3%

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

      2. neg-mul-1 65.3%

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

   10. Simplified 65.3%

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

   11. Taylor expanded in t around 0 52.5%

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

       1. associate-/l* 65.3%

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

   13. Simplified 65.3%

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

   if -3.49999999999999983e-178 < a < -3.19999999999999988e-259

   1. Initial program 79.3%

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

      1. associate-/l* 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in z around inf 79.0%

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

      1. associate--l+ 79.0%

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

      2. associate-*r/ 79.0%

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

      3. associate-*r/ 79.0%

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

      4. mul-1-neg 79.0%

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

      5. div-sub 79.0%

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

      6. mul-1-neg 79.0%

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

      7. distribute-lft-out-- 79.0%

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

      8. associate-*r/ 79.0%

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

      9. mul-1-neg 79.0%

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

      10. unsub-neg 79.0%

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

      11. distribute-rgt-out-- 79.0%

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

   7. Simplified 79.0%

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

   8. Taylor expanded in t around 0 58.1%

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

      1. associate-/l* 64.9%

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

   10. Simplified 64.9%

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

   11. Taylor expanded in y around inf 58.1%

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

       1. associate-/l* 64.9%

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

   13. Simplified 64.9%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-178}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-259}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-28}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z}\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-259}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) z))))
   (if (<= a -4.2e+38)
     x
     (if (<= a -3.5e-178)
       t_1
       (if (<= a -3.7e-259) (* x (/ y z)) (if (<= a 3.9e+80) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double tmp;
	if (a <= -4.2e+38) {
		tmp = x;
	} else if (a <= -3.5e-178) {
		tmp = t_1;
	} else if (a <= -3.7e-259) {
		tmp = x * (y / z);
	} else if (a <= 3.9e+80) {
		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 * ((z - y) / z)
    if (a <= (-4.2d+38)) then
        tmp = x
    else if (a <= (-3.5d-178)) then
        tmp = t_1
    else if (a <= (-3.7d-259)) then
        tmp = x * (y / z)
    else if (a <= 3.9d+80) 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 * ((z - y) / z);
	double tmp;
	if (a <= -4.2e+38) {
		tmp = x;
	} else if (a <= -3.5e-178) {
		tmp = t_1;
	} else if (a <= -3.7e-259) {
		tmp = x * (y / z);
	} else if (a <= 3.9e+80) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / z)
	tmp = 0
	if a <= -4.2e+38:
		tmp = x
	elif a <= -3.5e-178:
		tmp = t_1
	elif a <= -3.7e-259:
		tmp = x * (y / z)
	elif a <= 3.9e+80:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / z))
	tmp = 0.0
	if (a <= -4.2e+38)
		tmp = x;
	elseif (a <= -3.5e-178)
		tmp = t_1;
	elseif (a <= -3.7e-259)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 3.9e+80)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / z);
	tmp = 0.0;
	if (a <= -4.2e+38)
		tmp = x;
	elseif (a <= -3.5e-178)
		tmp = t_1;
	elseif (a <= -3.7e-259)
		tmp = x * (y / z);
	elseif (a <= 3.9e+80)
		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[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.2e+38], x, If[LessEqual[a, -3.5e-178], t$95$1, If[LessEqual[a, -3.7e-259], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.9e+80], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.2e38 or 3.89999999999999999e80 < a

   1. Initial program 66.3%

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

      1. associate-/l* 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in a around inf 48.9%

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

   if -4.2e38 < a < -3.49999999999999983e-178 or -3.69999999999999991e-259 < a < 3.89999999999999999e80

   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* 73.8%

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

   3. Simplified 73.8%

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

   5. Taylor expanded in x around 0 53.6%

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

      1. associate-/l* 67.0%

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

   7. Simplified 67.0%

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

   8. Taylor expanded in a around 0 59.0%

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

      1. associate-*r/ 59.0%

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

      2. neg-mul-1 59.0%

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

   10. Simplified 59.0%

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

   11. Taylor expanded in t around 0 45.7%

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

       1. associate-/l* 59.0%

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

   13. Simplified 59.0%

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

   if -3.49999999999999983e-178 < a < -3.69999999999999991e-259

   1. Initial program 79.3%

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

      1. associate-/l* 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in z around inf 79.0%

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

      1. associate--l+ 79.0%

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

      2. associate-*r/ 79.0%

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

      3. associate-*r/ 79.0%

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

      4. mul-1-neg 79.0%

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

      5. div-sub 79.0%

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

      6. mul-1-neg 79.0%

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

      7. distribute-lft-out-- 79.0%

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

      8. associate-*r/ 79.0%

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

      9. mul-1-neg 79.0%

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

      10. unsub-neg 79.0%

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

      11. distribute-rgt-out-- 79.0%

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

   7. Simplified 79.0%

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

   8. Taylor expanded in t around 0 58.1%

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

      1. associate-/l* 64.9%

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

   10. Simplified 64.9%

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

   11. Taylor expanded in y around inf 58.1%

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

       1. associate-/l* 64.9%

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

   13. Simplified 64.9%

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

Alternative 12: 81.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+33} \lor \neg \left(a \leq 4.2 \cdot 10^{-159}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6.2e+33) (not (<= a 4.2e-159)))
   (+ x (* (- y z) (/ (- t x) (- a z))))
   (+ t (* y (/ (- x t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.2e+33) || !(a <= 4.2e-159)) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = t + (y * ((x - t) / 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 <= (-6.2d+33)) .or. (.not. (a <= 4.2d-159))) then
        tmp = x + ((y - z) * ((t - x) / (a - z)))
    else
        tmp = t + (y * ((x - t) / 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 <= -6.2e+33) || !(a <= 4.2e-159)) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -6.2e+33) or not (a <= 4.2e-159):
		tmp = x + ((y - z) * ((t - x) / (a - z)))
	else:
		tmp = t + (y * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6.2e+33) || !(a <= 4.2e-159))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -6.2e+33) || ~((a <= 4.2e-159)))
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	else
		tmp = t + (y * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -6.2e+33], N[Not[LessEqual[a, 4.2e-159]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.2e33 or 4.1999999999999998e-159 < a

   1. Initial program 64.1%

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

      1. associate-/l* 86.5%

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

   3. Simplified 86.5%

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

   if -6.2e33 < a < 4.1999999999999998e-159

   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* 70.2%

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

   3. Simplified 70.2%

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

   5. Taylor expanded in z around inf 85.5%

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

      1. associate--l+ 85.5%

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

      2. associate-*r/ 85.5%

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

      3. associate-*r/ 85.5%

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

      4. mul-1-neg 85.5%

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

      5. div-sub 85.5%

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

      6. mul-1-neg 85.5%

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

      7. distribute-lft-out-- 85.5%

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

      8. associate-*r/ 85.5%

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

      9. mul-1-neg 85.5%

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

      10. unsub-neg 85.5%

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

      11. distribute-rgt-out-- 85.5%

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

   7. Simplified 85.5%

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

   8. Taylor expanded in y around inf 84.9%

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

      1. associate-/l* 87.6%

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

   10. Simplified 87.6%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+33} \lor \neg \left(a \leq 4.2 \cdot 10^{-159}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 69.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -125 \lor \neg \left(z \leq 2.5 \cdot 10^{+21}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -125.0) (not (<= z 2.5e+21)))
   (+ t (* y (/ (- x t) z)))
   (- x (* y (/ (- x t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -125.0) || !(z <= 2.5e+21)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x - (y * ((x - t) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-125.0d0)) .or. (.not. (z <= 2.5d+21))) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = x - (y * ((x - t) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -125.0) || !(z <= 2.5e+21)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x - (y * ((x - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -125.0) or not (z <= 2.5e+21):
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = x - (y * ((x - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -125.0) || !(z <= 2.5e+21))
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x - Float64(y * Float64(Float64(x - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -125.0) || ~((z <= 2.5e+21)))
		tmp = t + (y * ((x - t) / z));
	else
		tmp = x - (y * ((x - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -125.0], N[Not[LessEqual[z, 2.5e+21]], $MachinePrecision]], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -125 or 2.5e21 < z

   1. Initial program 43.9%

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

      1. associate-/l* 65.3%

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

   3. Simplified 65.3%

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

   5. Taylor expanded in z around inf 65.9%

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

      1. associate--l+ 65.9%

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

      2. associate-*r/ 65.9%

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

      3. associate-*r/ 65.9%

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

      4. mul-1-neg 65.9%

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

      5. div-sub 65.9%

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

      6. mul-1-neg 65.9%

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

      7. distribute-lft-out-- 65.9%

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

      8. associate-*r/ 65.9%

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

      9. mul-1-neg 65.9%

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

      10. unsub-neg 65.9%

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

      11. distribute-rgt-out-- 66.8%

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

   7. Simplified 66.8%

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

   8. Taylor expanded in y around inf 63.7%

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

      1. associate-/l* 74.5%

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

   10. Simplified 74.5%

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

   if -125 < z < 2.5e21

   1. Initial program 93.0%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in z around 0 71.7%

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

      1. associate-/l* 77.7%

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

   7. Simplified 77.7%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -125 \lor \neg \left(z \leq 2.5 \cdot 10^{+21}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -140:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+21}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -140.0)
   (+ t (* x (/ y z)))
   (if (<= z 2.8e+21) (- x (* y (/ (- x t) a))) (* t (/ (- y z) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -140.0) {
		tmp = t + (x * (y / z));
	} else if (z <= 2.8e+21) {
		tmp = x - (y * ((x - t) / a));
	} 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 (z <= (-140.0d0)) then
        tmp = t + (x * (y / z))
    else if (z <= 2.8d+21) then
        tmp = x - (y * ((x - t) / a))
    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 (z <= -140.0) {
		tmp = t + (x * (y / z));
	} else if (z <= 2.8e+21) {
		tmp = x - (y * ((x - t) / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -140.0:
		tmp = t + (x * (y / z))
	elif z <= 2.8e+21:
		tmp = x - (y * ((x - t) / a))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -140.0)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	elseif (z <= 2.8e+21)
		tmp = Float64(x - Float64(y * Float64(Float64(x - t) / a)));
	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 (z <= -140.0)
		tmp = t + (x * (y / z));
	elseif (z <= 2.8e+21)
		tmp = x - (y * ((x - t) / a));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -140.0], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+21], N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -140

   1. Initial program 46.0%

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

      1. associate-/l* 62.9%

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

   3. Simplified 62.9%

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

   5. Taylor expanded in z around inf 65.5%

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

      1. associate--l+ 65.5%

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

      2. associate-*r/ 65.5%

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

      3. associate-*r/ 65.5%

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

      4. mul-1-neg 65.5%

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

      5. div-sub 65.5%

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

      6. mul-1-neg 65.5%

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

      7. distribute-lft-out-- 65.5%

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

      8. associate-*r/ 65.5%

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

      9. mul-1-neg 65.5%

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

      10. unsub-neg 65.5%

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

      11. distribute-rgt-out-- 65.5%

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

   7. Simplified 65.5%

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

   8. Taylor expanded in y around inf 63.2%

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

   9. Taylor expanded in t around 0 54.9%

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

       1. mul-1-neg 54.9%

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

       2. associate-/l* 60.6%

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

       3. distribute-rgt-neg-in 60.6%

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

       4. distribute-neg-frac2 60.6%

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

   11. Simplified 60.6%

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

   if -140 < z < 2.8e21

   1. Initial program 93.0%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in z around 0 71.7%

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

      1. associate-/l* 77.7%

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

   7. Simplified 77.7%

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

   if 2.8e21 < z

   1. Initial program 41.0%

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

      1. associate-/l* 68.6%

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

   3. Simplified 68.6%

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

   5. Taylor expanded in x around 0 47.1%

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

      1. associate-/l* 71.5%

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

   7. Simplified 71.5%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -140:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+21}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 38.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.35e+72) t (if (<= z 3.6e+14) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+72) {
		tmp = t;
	} else if (z <= 3.6e+14) {
		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 <= (-1.35d+72)) then
        tmp = t
    else if (z <= 3.6d+14) 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 <= -1.35e+72) {
		tmp = t;
	} else if (z <= 3.6e+14) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.35e+72:
		tmp = t
	elif z <= 3.6e+14:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.35e+72)
		tmp = t;
	elseif (z <= 3.6e+14)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.35e+72)
		tmp = t;
	elseif (z <= 3.6e+14)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.35e+72], t, If[LessEqual[z, 3.6e+14], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e72 or 3.6e14 < z

   1. Initial program 39.5%

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

      1. associate-/l* 64.0%

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

   3. Simplified 64.0%

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

   5. Taylor expanded in z around inf 45.3%

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

   if -1.35e72 < z < 3.6e14

   1. Initial program 91.0%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in a around inf 34.1%

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

Alternative 16: 24.8% 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 66.9%

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

   1. associate-/l* 79.7%

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

3. Simplified 79.7%

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

5. Taylor expanded in z around inf 24.7%

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

Developer target: 84.5% 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 2024096 
(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))))