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

Percentage Accurate: 67.2% → 90.2%

Time: 16.7s

Alternatives: 18

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-248} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -5e-248) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (- t (/ (* (- t x) (- y a)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -5e-248) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = t - (((t - x) * (y - a)) / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -5e-248) || !(t_1 <= 0.0))
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(t - Float64(Float64(Float64(t - x) * Float64(y - a)) / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-248], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(t - N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $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))) < -5.0000000000000001e-248 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 76.8%

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

      1. +-commutative 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-/l* 90.7%

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

      4. fma-define 90.7%

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

   3. Simplified 90.7%

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

   if -5.0000000000000001e-248 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.7%

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

      1. +-commutative 4.7%

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

      2. *-commutative 4.7%

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

      3. associate-/l* 4.7%

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

      4. fma-define 4.7%

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

   3. Simplified 4.7%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. div-sub 99.8%

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

      6. mul-1-neg 99.8%

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

      7. distribute-lft-out-- 99.8%

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

      8. associate-*r/ 99.8%

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

      9. mul-1-neg 99.8%

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

      10. unsub-neg 99.8%

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

      11. distribute-rgt-out-- 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -5 \cdot 10^{-248} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 10^{+223}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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-248)
     t_1
     (if (<= t_2 0.0)
       (- t (/ (* (- t x) (- y a)) z))
       (if (<= t_2 1e+223) 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-248) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t - (((t - x) * (y - a)) / z);
	} else if (t_2 <= 1e+223) {
		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-248)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = t - (((t - x) * (y - a)) / z)
    else if (t_2 <= 1d+223) 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-248) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t - (((t - x) * (y - a)) / z);
	} else if (t_2 <= 1e+223) {
		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-248:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = t - (((t - x) * (y - a)) / z)
	elif t_2 <= 1e+223:
		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-248)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t - Float64(Float64(Float64(t - x) * Float64(y - a)) / z));
	elseif (t_2 <= 1e+223)
		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-248)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = t - (((t - x) * (y - a)) / z);
	elseif (t_2 <= 1e+223)
		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-248], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t - N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+223], 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))) < -5.0000000000000001e-248 or 1.00000000000000005e223 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   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* 87.8%

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

   3. Simplified 87.8%

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

   if -5.0000000000000001e-248 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.7%

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

      1. +-commutative 4.7%

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

      2. *-commutative 4.7%

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

      3. associate-/l* 4.7%

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

      4. fma-define 4.7%

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

   3. Simplified 4.7%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. div-sub 99.8%

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

      6. mul-1-neg 99.8%

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

      7. distribute-lft-out-- 99.8%

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

      8. associate-*r/ 99.8%

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

      9. mul-1-neg 99.8%

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

      10. unsub-neg 99.8%

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

      11. distribute-rgt-out-- 99.8%

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

   7. Simplified 99.8%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 1.00000000000000005e223

   1. Initial program 96.5%

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

Alternative 3: 37.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -3.1 \cdot 10^{+155}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.4 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-261}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-211}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) a))))
   (if (<= a -3.1e+155)
     x
     (if (<= a -8.4e-128)
       t_1
       (if (<= a 1.25e-261)
         t
         (if (<= a 6.5e-211)
           (* y (/ t (- a z)))
           (if (<= a 3.5e+121) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (a <= -3.1e+155) {
		tmp = x;
	} else if (a <= -8.4e-128) {
		tmp = t_1;
	} else if (a <= 1.25e-261) {
		tmp = t;
	} else if (a <= 6.5e-211) {
		tmp = y * (t / (a - z));
	} else if (a <= 3.5e+121) {
		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 = y * ((t - x) / a)
    if (a <= (-3.1d+155)) then
        tmp = x
    else if (a <= (-8.4d-128)) then
        tmp = t_1
    else if (a <= 1.25d-261) then
        tmp = t
    else if (a <= 6.5d-211) then
        tmp = y * (t / (a - z))
    else if (a <= 3.5d+121) 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 = y * ((t - x) / a);
	double tmp;
	if (a <= -3.1e+155) {
		tmp = x;
	} else if (a <= -8.4e-128) {
		tmp = t_1;
	} else if (a <= 1.25e-261) {
		tmp = t;
	} else if (a <= 6.5e-211) {
		tmp = y * (t / (a - z));
	} else if (a <= 3.5e+121) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / a)
	tmp = 0
	if a <= -3.1e+155:
		tmp = x
	elif a <= -8.4e-128:
		tmp = t_1
	elif a <= 1.25e-261:
		tmp = t
	elif a <= 6.5e-211:
		tmp = y * (t / (a - z))
	elif a <= 3.5e+121:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (a <= -3.1e+155)
		tmp = x;
	elseif (a <= -8.4e-128)
		tmp = t_1;
	elseif (a <= 1.25e-261)
		tmp = t;
	elseif (a <= 6.5e-211)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (a <= 3.5e+121)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / a);
	tmp = 0.0;
	if (a <= -3.1e+155)
		tmp = x;
	elseif (a <= -8.4e-128)
		tmp = t_1;
	elseif (a <= 1.25e-261)
		tmp = t;
	elseif (a <= 6.5e-211)
		tmp = y * (t / (a - z));
	elseif (a <= 3.5e+121)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.1e+155], x, If[LessEqual[a, -8.4e-128], t$95$1, If[LessEqual[a, 1.25e-261], t, If[LessEqual[a, 6.5e-211], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e+121], t$95$1, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.09999999999999989e155 or 3.5e121 < a

   1. Initial program 72.9%

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

      1. +-commutative 72.9%

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

      2. *-commutative 72.9%

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

      3. associate-/l* 91.5%

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

      4. fma-define 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in a around inf 59.2%

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

   if -3.09999999999999989e155 < a < -8.4000000000000004e-128 or 6.4999999999999996e-211 < a < 3.5e121

   1. Initial program 75.4%

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

      1. +-commutative 75.4%

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

      2. *-commutative 75.4%

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

      3. associate-/l* 87.0%

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

      4. fma-define 87.0%

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

   3. Simplified 87.0%

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

      1. add-cube-cbrt 85.9%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}, \frac{y - z}{a - z}, x\right) \]

      2. pow3 85.9%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   6. Applied egg-rr 85.9%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   7. Taylor expanded in y around inf 60.9%

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

      1. div-sub 61.7%

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

   9. Simplified 61.7%

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

   10. Taylor expanded in a around inf 46.5%

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

   if -8.4000000000000004e-128 < a < 1.24999999999999995e-261

   1. Initial program 68.6%

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

      1. +-commutative 68.6%

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

      2. *-commutative 68.6%

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

      3. associate-/l* 77.8%

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

      4. fma-define 77.7%

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

   3. Simplified 77.7%

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

      1. add-cube-cbrt 76.3%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}, \frac{y - z}{a - z}, x\right) \]

      2. pow3 76.3%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   6. Applied egg-rr 76.3%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   7. Taylor expanded in z around inf 44.1%

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

   if 1.24999999999999995e-261 < a < 6.4999999999999996e-211

   1. Initial program 70.8%

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

      1. +-commutative 70.8%

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

      2. *-commutative 70.8%

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

      3. associate-/l* 82.5%

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

      4. fma-define 82.5%

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

   3. Simplified 82.5%

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

      1. add-cube-cbrt 82.4%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}, \frac{y - z}{a - z}, x\right) \]

      2. pow3 82.4%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   6. Applied egg-rr 82.4%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   7. Taylor expanded in y around inf 91.2%

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

      1. div-sub 91.2%

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

   9. Simplified 91.2%

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

   10. Taylor expanded in t around inf 65.3%

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

Alternative 4: 61.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -2.55 \cdot 10^{-40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-224}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-57}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (* y (/ (- t x) a)))))
   (if (<= a -2.55e-40)
     t_2
     (if (<= a 3.9e-224)
       t_1
       (if (<= a 2.5e-57)
         (/ y (/ (- a z) (- t x)))
         (if (<= a 1.3e+69) 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 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -2.55e-40) {
		tmp = t_2;
	} else if (a <= 3.9e-224) {
		tmp = t_1;
	} else if (a <= 2.5e-57) {
		tmp = y / ((a - z) / (t - x));
	} else if (a <= 1.3e+69) {
		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 = x + (y * ((t - x) / a))
    if (a <= (-2.55d-40)) then
        tmp = t_2
    else if (a <= 3.9d-224) then
        tmp = t_1
    else if (a <= 2.5d-57) then
        tmp = y / ((a - z) / (t - x))
    else if (a <= 1.3d+69) 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 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -2.55e-40) {
		tmp = t_2;
	} else if (a <= 3.9e-224) {
		tmp = t_1;
	} else if (a <= 2.5e-57) {
		tmp = y / ((a - z) / (t - x));
	} else if (a <= 1.3e+69) {
		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 = x + (y * ((t - x) / a))
	tmp = 0
	if a <= -2.55e-40:
		tmp = t_2
	elif a <= 3.9e-224:
		tmp = t_1
	elif a <= 2.5e-57:
		tmp = y / ((a - z) / (t - x))
	elif a <= 1.3e+69:
		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(x + Float64(y * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -2.55e-40)
		tmp = t_2;
	elseif (a <= 3.9e-224)
		tmp = t_1;
	elseif (a <= 2.5e-57)
		tmp = Float64(y / Float64(Float64(a - z) / Float64(t - x)));
	elseif (a <= 1.3e+69)
		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 = x + (y * ((t - x) / a));
	tmp = 0.0;
	if (a <= -2.55e-40)
		tmp = t_2;
	elseif (a <= 3.9e-224)
		tmp = t_1;
	elseif (a <= 2.5e-57)
		tmp = y / ((a - z) / (t - x));
	elseif (a <= 1.3e+69)
		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[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.55e-40], t$95$2, If[LessEqual[a, 3.9e-224], t$95$1, If[LessEqual[a, 2.5e-57], N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e+69], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.55000000000000019e-40 or 1.3000000000000001e69 < a

   1. Initial program 74.6%

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

      1. associate-/l* 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in z around 0 68.2%

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

      1. associate-/l* 76.0%

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

   7. Simplified 76.0%

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

   if -2.55000000000000019e-40 < a < 3.8999999999999998e-224 or 2.5000000000000001e-57 < a < 1.3000000000000001e69

   1. Initial program 69.9%

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

      1. +-commutative 69.9%

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

      2. *-commutative 69.9%

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

      3. associate-/l* 81.9%

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

      4. fma-define 81.8%

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

   3. Simplified 81.8%

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

      1. add-cube-cbrt 80.3%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}, \frac{y - z}{a - z}, x\right) \]

      2. pow3 80.3%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   6. Applied egg-rr 80.3%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   7. Taylor expanded in t around inf 68.4%

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

      1. div-sub 68.4%

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

   9. Simplified 68.4%

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

   if 3.8999999999999998e-224 < a < 2.5000000000000001e-57

   1. Initial program 77.7%

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

      1. +-commutative 77.7%

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

      2. *-commutative 77.7%

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

      3. associate-/l* 81.2%

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

      4. fma-define 81.3%

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

   3. Simplified 81.3%

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

      1. add-cube-cbrt 80.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}, \frac{y - z}{a - z}, x\right) \]

      2. pow3 80.9%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   6. Applied egg-rr 80.9%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   7. Taylor expanded in y around inf 85.7%

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

      1. div-sub 88.6%

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

   9. Simplified 88.6%

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

       1. clear-num 88.6%

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

       2. un-div-inv 88.6%

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

   11. Applied egg-rr 88.6%

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

Alternative 5: 61.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{-40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-225}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-58}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (* y (/ (- t x) a)))))
   (if (<= a -5.2e-40)
     t_2
     (if (<= a 3.9e-225)
       t_1
       (if (<= a 1.4e-58)
         (* y (/ (- t x) (- a z)))
         (if (<= a 3.2e+67) 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 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -5.2e-40) {
		tmp = t_2;
	} else if (a <= 3.9e-225) {
		tmp = t_1;
	} else if (a <= 1.4e-58) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 3.2e+67) {
		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 = x + (y * ((t - x) / a))
    if (a <= (-5.2d-40)) then
        tmp = t_2
    else if (a <= 3.9d-225) then
        tmp = t_1
    else if (a <= 1.4d-58) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 3.2d+67) 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 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -5.2e-40) {
		tmp = t_2;
	} else if (a <= 3.9e-225) {
		tmp = t_1;
	} else if (a <= 1.4e-58) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 3.2e+67) {
		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 = x + (y * ((t - x) / a))
	tmp = 0
	if a <= -5.2e-40:
		tmp = t_2
	elif a <= 3.9e-225:
		tmp = t_1
	elif a <= 1.4e-58:
		tmp = y * ((t - x) / (a - z))
	elif a <= 3.2e+67:
		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(x + Float64(y * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -5.2e-40)
		tmp = t_2;
	elseif (a <= 3.9e-225)
		tmp = t_1;
	elseif (a <= 1.4e-58)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 3.2e+67)
		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 = x + (y * ((t - x) / a));
	tmp = 0.0;
	if (a <= -5.2e-40)
		tmp = t_2;
	elseif (a <= 3.9e-225)
		tmp = t_1;
	elseif (a <= 1.4e-58)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 3.2e+67)
		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[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.2e-40], t$95$2, If[LessEqual[a, 3.9e-225], t$95$1, If[LessEqual[a, 1.4e-58], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e+67], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.2000000000000003e-40 or 3.19999999999999983e67 < a

   1. Initial program 74.6%

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

      1. associate-/l* 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in z around 0 68.2%

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

      1. associate-/l* 76.0%

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

   7. Simplified 76.0%

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

   if -5.2000000000000003e-40 < a < 3.9e-225 or 1.4e-58 < a < 3.19999999999999983e67

   1. Initial program 69.9%

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

      1. +-commutative 69.9%

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

      2. *-commutative 69.9%

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

      3. associate-/l* 81.9%

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

      4. fma-define 81.8%

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

   3. Simplified 81.8%

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

      1. add-cube-cbrt 80.3%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}, \frac{y - z}{a - z}, x\right) \]

      2. pow3 80.3%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   6. Applied egg-rr 80.3%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   7. Taylor expanded in t around inf 68.4%

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

      1. div-sub 68.4%

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

   9. Simplified 68.4%

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

   if 3.9e-225 < a < 1.4e-58

   1. Initial program 77.7%

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

      1. +-commutative 77.7%

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

      2. *-commutative 77.7%

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

      3. associate-/l* 81.2%

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

      4. fma-define 81.3%

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

   3. Simplified 81.3%

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

      1. add-cube-cbrt 80.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}, \frac{y - z}{a - z}, x\right) \]

      2. pow3 80.9%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   6. Applied egg-rr 80.9%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   7. Taylor expanded in y around inf 85.7%

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

      1. div-sub 88.6%

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

   9. Simplified 88.6%

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

Alternative 6: 61.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + t \cdot \frac{y - z}{a}\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{-35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{-225}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (* t (/ (- y z) a)))))
   (if (<= a -1.05e-35)
     t_2
     (if (<= a 1.28e-225)
       t_1
       (if (<= a 3.9e-52)
         (* y (/ (- t x) (- a z)))
         (if (<= a 7.6e+69) 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 = x + (t * ((y - z) / a));
	double tmp;
	if (a <= -1.05e-35) {
		tmp = t_2;
	} else if (a <= 1.28e-225) {
		tmp = t_1;
	} else if (a <= 3.9e-52) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 7.6e+69) {
		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 = x + (t * ((y - z) / a))
    if (a <= (-1.05d-35)) then
        tmp = t_2
    else if (a <= 1.28d-225) then
        tmp = t_1
    else if (a <= 3.9d-52) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 7.6d+69) 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 = x + (t * ((y - z) / a));
	double tmp;
	if (a <= -1.05e-35) {
		tmp = t_2;
	} else if (a <= 1.28e-225) {
		tmp = t_1;
	} else if (a <= 3.9e-52) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 7.6e+69) {
		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 = x + (t * ((y - z) / a))
	tmp = 0
	if a <= -1.05e-35:
		tmp = t_2
	elif a <= 1.28e-225:
		tmp = t_1
	elif a <= 3.9e-52:
		tmp = y * ((t - x) / (a - z))
	elif a <= 7.6e+69:
		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(x + Float64(t * Float64(Float64(y - z) / a)))
	tmp = 0.0
	if (a <= -1.05e-35)
		tmp = t_2;
	elseif (a <= 1.28e-225)
		tmp = t_1;
	elseif (a <= 3.9e-52)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 7.6e+69)
		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 = x + (t * ((y - z) / a));
	tmp = 0.0;
	if (a <= -1.05e-35)
		tmp = t_2;
	elseif (a <= 1.28e-225)
		tmp = t_1;
	elseif (a <= 3.9e-52)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 7.6e+69)
		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[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.05e-35], t$95$2, If[LessEqual[a, 1.28e-225], t$95$1, If[LessEqual[a, 3.9e-52], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.6e+69], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.05e-35 or 7.60000000000000055e69 < a

   1. Initial program 74.6%

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

      1. associate-/l* 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in t around inf 70.4%

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

      1. associate-/l* 78.3%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in a around inf 68.4%

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

      1. associate-/l* 72.4%

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

   10. Simplified 72.4%

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

   if -1.05e-35 < a < 1.27999999999999993e-225 or 3.90000000000000018e-52 < a < 7.60000000000000055e69

   1. Initial program 69.9%

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

      1. +-commutative 69.9%

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

      2. *-commutative 69.9%

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

      3. associate-/l* 81.9%

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

      4. fma-define 81.8%

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

   3. Simplified 81.8%

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

      1. add-cube-cbrt 80.3%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}, \frac{y - z}{a - z}, x\right) \]

      2. pow3 80.3%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   6. Applied egg-rr 80.3%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   7. Taylor expanded in t around inf 68.4%

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

      1. div-sub 68.4%

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

   9. Simplified 68.4%

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

   if 1.27999999999999993e-225 < a < 3.90000000000000018e-52

   1. Initial program 77.7%

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

      1. +-commutative 77.7%

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

      2. *-commutative 77.7%

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

      3. associate-/l* 81.2%

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

      4. fma-define 81.3%

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

   3. Simplified 81.3%

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

      1. add-cube-cbrt 80.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}, \frac{y - z}{a - z}, x\right) \]

      2. pow3 80.9%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   6. Applied egg-rr 80.9%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   7. Taylor expanded in y around inf 85.7%

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

      1. div-sub 88.6%

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

   9. Simplified 88.6%

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

Alternative 7: 58.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -2.25 \cdot 10^{-36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-225}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (* t (/ y a)))))
   (if (<= a -2.25e-36)
     t_2
     (if (<= a 4.5e-225)
       t_1
       (if (<= a 3.1e-53)
         (* y (/ (- t x) (- a z)))
         (if (<= a 1.6e+69) 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 = x + (t * (y / a));
	double tmp;
	if (a <= -2.25e-36) {
		tmp = t_2;
	} else if (a <= 4.5e-225) {
		tmp = t_1;
	} else if (a <= 3.1e-53) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.6e+69) {
		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 = x + (t * (y / a))
    if (a <= (-2.25d-36)) then
        tmp = t_2
    else if (a <= 4.5d-225) then
        tmp = t_1
    else if (a <= 3.1d-53) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 1.6d+69) 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 = x + (t * (y / a));
	double tmp;
	if (a <= -2.25e-36) {
		tmp = t_2;
	} else if (a <= 4.5e-225) {
		tmp = t_1;
	} else if (a <= 3.1e-53) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.6e+69) {
		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 = x + (t * (y / a))
	tmp = 0
	if a <= -2.25e-36:
		tmp = t_2
	elif a <= 4.5e-225:
		tmp = t_1
	elif a <= 3.1e-53:
		tmp = y * ((t - x) / (a - z))
	elif a <= 1.6e+69:
		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(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (a <= -2.25e-36)
		tmp = t_2;
	elseif (a <= 4.5e-225)
		tmp = t_1;
	elseif (a <= 3.1e-53)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 1.6e+69)
		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 = x + (t * (y / a));
	tmp = 0.0;
	if (a <= -2.25e-36)
		tmp = t_2;
	elseif (a <= 4.5e-225)
		tmp = t_1;
	elseif (a <= 3.1e-53)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 1.6e+69)
		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[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.25e-36], t$95$2, If[LessEqual[a, 4.5e-225], t$95$1, If[LessEqual[a, 3.1e-53], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+69], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.25000000000000012e-36 or 1.59999999999999992e69 < a

   1. Initial program 74.6%

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

      1. associate-/l* 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in t around inf 70.4%

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

      1. associate-/l* 78.3%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in z around 0 64.1%

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

      1. associate-/l* 67.2%

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

   10. Simplified 67.2%

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

   if -2.25000000000000012e-36 < a < 4.5e-225 or 3.10000000000000015e-53 < a < 1.59999999999999992e69

   1. Initial program 69.9%

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

      1. +-commutative 69.9%

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

      2. *-commutative 69.9%

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

      3. associate-/l* 81.9%

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

      4. fma-define 81.8%

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

   3. Simplified 81.8%

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

      1. add-cube-cbrt 80.3%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}, \frac{y - z}{a - z}, x\right) \]

      2. pow3 80.3%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   6. Applied egg-rr 80.3%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   7. Taylor expanded in t around inf 68.4%

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

      1. div-sub 68.4%

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

   9. Simplified 68.4%

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

   if 4.5e-225 < a < 3.10000000000000015e-53

   1. Initial program 77.7%

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

      1. +-commutative 77.7%

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

      2. *-commutative 77.7%

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

      3. associate-/l* 81.2%

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

      4. fma-define 81.3%

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

   3. Simplified 81.3%

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

      1. add-cube-cbrt 80.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}, \frac{y - z}{a - z}, x\right) \]

      2. pow3 80.9%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   6. Applied egg-rr 80.9%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   7. Taylor expanded in y around inf 85.7%

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

      1. div-sub 88.6%

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

   9. Simplified 88.6%

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

Alternative 8: 82.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.25 \cdot 10^{+252}:\\ \;\;\;\;t - \left(x - t\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+225}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.25e+252)
   (- t (* (- x t) (/ a z)))
   (if (<= z 1.35e+225)
     (+ x (* (- y z) (/ (- t x) (- a z))))
     (+ t (* a (/ (- t x) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.25e+252) {
		tmp = t - ((x - t) * (a / z));
	} else if (z <= 1.35e+225) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = t + (a * ((t - x) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.25d+252)) then
        tmp = t - ((x - t) * (a / z))
    else if (z <= 1.35d+225) then
        tmp = x + ((y - z) * ((t - x) / (a - z)))
    else
        tmp = t + (a * ((t - x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.25e+252) {
		tmp = t - ((x - t) * (a / z));
	} else if (z <= 1.35e+225) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = t + (a * ((t - x) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.25e+252:
		tmp = t - ((x - t) * (a / z))
	elif z <= 1.35e+225:
		tmp = x + ((y - z) * ((t - x) / (a - z)))
	else:
		tmp = t + (a * ((t - x) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.25e+252)
		tmp = Float64(t - Float64(Float64(x - t) * Float64(a / z)));
	elseif (z <= 1.35e+225)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(a * Float64(Float64(t - x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.25e+252)
		tmp = t - ((x - t) * (a / z));
	elseif (z <= 1.35e+225)
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	else
		tmp = t + (a * ((t - x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.25e+252], N[(t - N[(N[(x - t), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+225], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(a * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.25e252

   1. Initial program 11.5%

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

      1. +-commutative 11.5%

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

      2. *-commutative 11.5%

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

      3. associate-/l* 47.7%

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

      4. fma-define 47.7%

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

   3. Simplified 47.7%

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

   5. Taylor expanded in y around 0 11.5%

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

      1. mul-1-neg 11.5%

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

      2. associate-/l* 43.5%

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

      3. distribute-lft-neg-out 43.5%

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

      4. +-commutative 43.5%

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

      5. *-commutative 43.5%

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

      6. fma-define 43.5%

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

   7. Simplified 43.5%

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

   8. Taylor expanded in z around -inf 39.8%

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

      1. mul-1-neg 39.8%

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

      2. unsub-neg 39.8%

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

      3. distribute-lft-out-- 41.2%

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

   10. Simplified 41.2%

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

       1. *-commutative 41.2%

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

       2. *-un-lft-identity 41.2%

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

       3. times-frac 74.3%

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

   12. Applied egg-rr 74.3%

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

   if -3.25e252 < z < 1.3499999999999999e225

   1. Initial program 78.5%

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

      1. associate-/l* 87.4%

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

   3. Simplified 87.4%

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

   if 1.3499999999999999e225 < z

   1. Initial program 36.1%

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

      1. +-commutative 36.1%

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

      2. *-commutative 36.1%

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

      3. associate-/l* 63.3%

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

      4. fma-define 62.9%

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

   3. Simplified 62.9%

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

   5. Taylor expanded in y around 0 36.1%

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

      1. mul-1-neg 36.1%

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

      2. associate-/l* 46.3%

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

      3. distribute-lft-neg-out 46.3%

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

      4. +-commutative 46.3%

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

      5. *-commutative 46.3%

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

      6. fma-define 46.0%

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

   7. Simplified 46.0%

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

   8. Taylor expanded in z around inf 83.9%

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

      1. associate-/l* 88.5%

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

   10. Simplified 88.5%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.25 \cdot 10^{+252}:\\ \;\;\;\;t - \left(x - t\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+225}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 35.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-262}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+121}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.1e-35)
   x
   (if (<= a 1.9e-262) t (if (<= a 3.1e+121) (* t (/ y (- a z))) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e-35) {
		tmp = x;
	} else if (a <= 1.9e-262) {
		tmp = t;
	} else if (a <= 3.1e+121) {
		tmp = t * (y / (a - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.1d-35)) then
        tmp = x
    else if (a <= 1.9d-262) then
        tmp = t
    else if (a <= 3.1d+121) then
        tmp = t * (y / (a - z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e-35) {
		tmp = x;
	} else if (a <= 1.9e-262) {
		tmp = t;
	} else if (a <= 3.1e+121) {
		tmp = t * (y / (a - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.1e-35:
		tmp = x
	elif a <= 1.9e-262:
		tmp = t
	elif a <= 3.1e+121:
		tmp = t * (y / (a - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.1e-35)
		tmp = x;
	elseif (a <= 1.9e-262)
		tmp = t;
	elseif (a <= 3.1e+121)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.1e-35)
		tmp = x;
	elseif (a <= 1.9e-262)
		tmp = t;
	elseif (a <= 3.1e+121)
		tmp = t * (y / (a - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.1e-35], x, If[LessEqual[a, 1.9e-262], t, If[LessEqual[a, 3.1e+121], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.09999999999999997e-35 or 3.10000000000000008e121 < a

   1. Initial program 73.5%

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

      1. +-commutative 73.5%

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

      2. *-commutative 73.5%

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

      3. associate-/l* 90.6%

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

      4. fma-define 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in a around inf 49.2%

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

   if -1.09999999999999997e-35 < a < 1.9000000000000001e-262

   1. Initial program 67.9%

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

      1. +-commutative 67.9%

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

      2. *-commutative 67.9%

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

      3. associate-/l* 76.2%

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

      4. fma-define 76.1%

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

   3. Simplified 76.1%

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

      1. add-cube-cbrt 74.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}, \frac{y - z}{a - z}, x\right) \]

      2. pow3 74.8%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   6. Applied egg-rr 74.8%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   7. Taylor expanded in z around inf 38.1%

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

   if 1.9000000000000001e-262 < a < 3.10000000000000008e121

   1. Initial program 77.1%

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

      1. +-commutative 77.1%

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

      2. *-commutative 77.1%

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

      3. associate-/l* 89.0%

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

      4. fma-define 89.0%

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

   3. Simplified 89.0%

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

      1. add-cube-cbrt 88.0%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}, \frac{y - z}{a - z}, x\right) \]

      2. pow3 88.1%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   6. Applied egg-rr 88.1%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   7. Taylor expanded in y around inf 72.8%

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

      1. div-sub 74.0%

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

   9. Simplified 74.0%

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

   10. Taylor expanded in t around inf 37.4%

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

       1. associate-/l* 42.5%

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

   12. Simplified 42.5%

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

Alternative 10: 36.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.65 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-262}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+68}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.65e-37)
   x
   (if (<= a 2.25e-262)
     t
     (if (<= a 1.25e-54) (* x (/ y z)) (if (<= a 1.85e+68) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.65e-37) {
		tmp = x;
	} else if (a <= 2.25e-262) {
		tmp = t;
	} else if (a <= 1.25e-54) {
		tmp = x * (y / z);
	} else if (a <= 1.85e+68) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.65d-37)) then
        tmp = x
    else if (a <= 2.25d-262) then
        tmp = t
    else if (a <= 1.25d-54) then
        tmp = x * (y / z)
    else if (a <= 1.85d+68) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.65e-37) {
		tmp = x;
	} else if (a <= 2.25e-262) {
		tmp = t;
	} else if (a <= 1.25e-54) {
		tmp = x * (y / z);
	} else if (a <= 1.85e+68) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.65e-37:
		tmp = x
	elif a <= 2.25e-262:
		tmp = t
	elif a <= 1.25e-54:
		tmp = x * (y / z)
	elif a <= 1.85e+68:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.65e-37)
		tmp = x;
	elseif (a <= 2.25e-262)
		tmp = t;
	elseif (a <= 1.25e-54)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.85e+68)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.65e-37)
		tmp = x;
	elseif (a <= 2.25e-262)
		tmp = t;
	elseif (a <= 1.25e-54)
		tmp = x * (y / z);
	elseif (a <= 1.85e+68)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.65e-37], x, If[LessEqual[a, 2.25e-262], t, If[LessEqual[a, 1.25e-54], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e+68], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.6499999999999998e-37 or 1.84999999999999999e68 < a

   1. Initial program 74.6%

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

      1. +-commutative 74.6%

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

      2. *-commutative 74.6%

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

      3. associate-/l* 91.5%

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

      4. fma-define 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in a around inf 47.5%

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

   if -3.6499999999999998e-37 < a < 2.24999999999999999e-262 or 1.25000000000000004e-54 < a < 1.84999999999999999e68

   1. Initial program 69.7%

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

      1. +-commutative 69.7%

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

      2. *-commutative 69.7%

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

      3. associate-/l* 81.6%

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

      4. fma-define 81.4%

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

   3. Simplified 81.4%

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

      1. add-cube-cbrt 80.0%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}, \frac{y - z}{a - z}, x\right) \]

      2. pow3 79.9%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   6. Applied egg-rr 79.9%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   7. Taylor expanded in z around inf 37.2%

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

   if 2.24999999999999999e-262 < a < 1.25000000000000004e-54

   1. Initial program 76.9%

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

      1. +-commutative 76.9%

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

      2. *-commutative 76.9%

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

      3. associate-/l* 82.1%

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

      4. fma-define 82.2%

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

   3. Simplified 82.2%

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

      1. add-cube-cbrt 81.5%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}, \frac{y - z}{a - z}, x\right) \]

      2. pow3 81.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   6. Applied egg-rr 81.7%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   7. Taylor expanded in y around inf 85.7%

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

      1. div-sub 88.2%

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

   9. Simplified 88.2%

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

   10. Taylor expanded in t around 0 55.3%

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

       1. mul-1-neg 55.3%

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

       2. associate-/l* 57.6%

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

       3. distribute-lft-neg-in 57.6%

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

   12. Simplified 57.6%

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

   13. Taylor expanded in a around 0 43.5%

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

       1. associate-/l* 48.1%

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

   15. Simplified 48.1%

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

Alternative 11: 73.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+115} \lor \neg \left(y \leq 2.4 \cdot 10^{+90}\right):\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5.8e+115) (not (<= y 2.4e+90)))
   (* y (/ (- t x) (- a z)))
   (+ x (* t (/ (- y z) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.8e+115) || !(y <= 2.4e+90)) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = x + (t * ((y - z) / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-5.8d+115)) .or. (.not. (y <= 2.4d+90))) then
        tmp = y * ((t - x) / (a - z))
    else
        tmp = x + (t * ((y - z) / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.8e+115) || !(y <= 2.4e+90)) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = x + (t * ((y - z) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5.8e+115) or not (y <= 2.4e+90):
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = x + (t * ((y - z) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5.8e+115) || !(y <= 2.4e+90))
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -5.8e+115) || ~((y <= 2.4e+90)))
		tmp = y * ((t - x) / (a - z));
	else
		tmp = x + (t * ((y - z) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5.8e+115], N[Not[LessEqual[y, 2.4e+90]], $MachinePrecision]], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.80000000000000009e115 or 2.4000000000000001e90 < y

   1. Initial program 78.0%

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

      1. +-commutative 78.0%

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

      2. *-commutative 78.0%

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

      3. associate-/l* 91.3%

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

      4. fma-define 91.2%

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

   3. Simplified 91.2%

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

      1. add-cube-cbrt 90.4%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}, \frac{y - z}{a - z}, x\right) \]

      2. pow3 90.4%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   6. Applied egg-rr 90.4%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   7. Taylor expanded in y around inf 82.6%

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

      1. div-sub 82.6%

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

   9. Simplified 82.6%

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

   if -5.80000000000000009e115 < y < 2.4000000000000001e90

   1. Initial program 70.4%

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

      1. associate-/l* 80.6%

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

   3. Simplified 80.6%

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

   5. Taylor expanded in t around inf 64.1%

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

      1. associate-/l* 73.1%

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

   7. Simplified 73.1%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+115} \lor \neg \left(y \leq 2.4 \cdot 10^{+90}\right):\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 73.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+116}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq 19000000000:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5.6e+116)
   (* y (/ (- t x) (- a z)))
   (if (<= y 19000000000.0)
     (+ x (* t (/ (- y z) (- a z))))
     (+ x (/ y (/ (- a z) (- t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.6e+116) {
		tmp = y * ((t - x) / (a - z));
	} else if (y <= 19000000000.0) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = x + (y / ((a - z) / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-5.6d+116)) then
        tmp = y * ((t - x) / (a - z))
    else if (y <= 19000000000.0d0) then
        tmp = x + (t * ((y - z) / (a - z)))
    else
        tmp = x + (y / ((a - z) / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.6e+116) {
		tmp = y * ((t - x) / (a - z));
	} else if (y <= 19000000000.0) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = x + (y / ((a - z) / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5.6e+116:
		tmp = y * ((t - x) / (a - z))
	elif y <= 19000000000.0:
		tmp = x + (t * ((y - z) / (a - z)))
	else:
		tmp = x + (y / ((a - z) / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5.6e+116)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (y <= 19000000000.0)
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -5.6e+116)
		tmp = y * ((t - x) / (a - z));
	elseif (y <= 19000000000.0)
		tmp = x + (t * ((y - z) / (a - z)));
	else
		tmp = x + (y / ((a - z) / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5.6e+116], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 19000000000.0], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.60000000000000009e116

   1. Initial program 73.9%

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

      1. +-commutative 73.9%

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

      2. *-commutative 73.9%

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

      3. associate-/l* 91.0%

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

      4. fma-define 90.9%

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

   3. Simplified 90.9%

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

      1. add-cube-cbrt 89.8%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}, \frac{y - z}{a - z}, x\right) \]

      2. pow3 89.8%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   6. Applied egg-rr 89.8%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   7. Taylor expanded in y around inf 87.5%

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

      1. div-sub 87.5%

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

   9. Simplified 87.5%

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

   if -5.60000000000000009e116 < y < 1.9e10

   1. Initial program 69.3%

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

      1. associate-/l* 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 t around inf 63.4%

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

      1. associate-/l* 72.9%

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

   7. Simplified 72.9%

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

   if 1.9e10 < y

   1. Initial program 81.1%

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

      1. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

      1. clear-num 91.4%

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

      2. un-div-inv 91.2%

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

   6. Applied egg-rr 91.2%

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

   7. Taylor expanded in y around inf 87.1%

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

Alternative 13: 60.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{-19} \lor \neg \left(x \leq 2.3 \cdot 10^{+45}\right):\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -7.4e-19) (not (<= x 2.3e+45)))
   (- x (* x (/ y a)))
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -7.4e-19) || !(x <= 2.3e+45)) {
		tmp = x - (x * (y / 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 ((x <= (-7.4d-19)) .or. (.not. (x <= 2.3d+45))) then
        tmp = x - (x * (y / 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 ((x <= -7.4e-19) || !(x <= 2.3e+45)) {
		tmp = x - (x * (y / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -7.4e-19) or not (x <= 2.3e+45):
		tmp = x - (x * (y / a))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -7.4e-19) || !(x <= 2.3e+45))
		tmp = Float64(x - Float64(x * Float64(y / 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 ((x <= -7.4e-19) || ~((x <= 2.3e+45)))
		tmp = x - (x * (y / a));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -7.4e-19], N[Not[LessEqual[x, 2.3e+45]], $MachinePrecision]], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.40000000000000011e-19 or 2.30000000000000012e45 < x

   1. Initial program 64.3%

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

      1. +-commutative 64.3%

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

      2. *-commutative 64.3%

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

      3. associate-/l* 83.2%

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

      4. fma-define 83.1%

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

   3. Simplified 83.1%

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

      1. add-cube-cbrt 82.5%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}, \frac{y - z}{a - z}, x\right) \]

      2. pow3 82.5%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   6. Applied egg-rr 82.5%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   7. Taylor expanded in t around 0 55.5%

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

      1. mul-1-neg 55.5%

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

      2. unsub-neg 55.5%

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

      3. associate-/l* 65.8%

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

   9. Simplified 65.8%

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

   10. Taylor expanded in z around 0 53.2%

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

       1. associate-/l* 58.9%

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

   12. Simplified 58.9%

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

   if -7.40000000000000011e-19 < x < 2.30000000000000012e45

   1. Initial program 82.2%

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

      1. +-commutative 82.2%

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

      2. *-commutative 82.2%

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

      3. associate-/l* 89.5%

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

      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
   5. Step-by-step derivation

      1. add-cube-cbrt 88.2%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}, \frac{y - z}{a - z}, x\right) \]

      2. pow3 88.3%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   6. Applied egg-rr 88.3%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   7. Taylor expanded in t around inf 70.8%

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

      1. div-sub 70.8%

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

   9. Simplified 70.8%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{-19} \lor \neg \left(x \leq 2.3 \cdot 10^{+45}\right):\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 54.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1200000000 \lor \neg \left(z \leq 8 \cdot 10^{+128}\right):\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1200000000.0) (not (<= z 8e+128)))
   (- t (/ (* x a) z))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1200000000.0) || !(z <= 8e+128)) {
		tmp = t - ((x * a) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1200000000.0d0)) .or. (.not. (z <= 8d+128))) then
        tmp = t - ((x * a) / z)
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1200000000.0) || !(z <= 8e+128)) {
		tmp = t - ((x * a) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1200000000.0) or not (z <= 8e+128):
		tmp = t - ((x * a) / z)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1200000000.0) || !(z <= 8e+128))
		tmp = Float64(t - Float64(Float64(x * a) / z));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1200000000.0) || ~((z <= 8e+128)))
		tmp = t - ((x * a) / z);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1200000000.0], N[Not[LessEqual[z, 8e+128]], $MachinePrecision]], N[(t - N[(N[(x * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e9 or 8.0000000000000006e128 < z

   1. Initial program 39.2%

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

      1. +-commutative 39.2%

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

      2. *-commutative 39.2%

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

      3. associate-/l* 70.1%

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

      4. fma-define 70.0%

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

   3. Simplified 70.0%

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

   5. Taylor expanded in y around 0 24.5%

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

      1. mul-1-neg 24.5%

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

      2. associate-/l* 42.6%

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

      3. distribute-lft-neg-out 42.6%

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

      4. +-commutative 42.6%

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

      5. *-commutative 42.6%

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

      6. fma-define 42.7%

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

   7. Simplified 42.7%

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

   8. Taylor expanded in z around -inf 49.7%

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

      1. mul-1-neg 49.7%

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

      2. unsub-neg 49.7%

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

      3. distribute-lft-out-- 50.1%

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

   10. Simplified 50.1%

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

   11. Taylor expanded in x around inf 48.9%

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

       1. *-commutative 48.9%

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

   13. Simplified 48.9%

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

   if -1.2e9 < z < 8.0000000000000006e128

   1. Initial program 91.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 t around inf 71.9%

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

      1. associate-/l* 74.1%

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

   7. Simplified 74.1%

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

   8. Taylor expanded in z around 0 57.1%

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

      1. associate-/l* 60.8%

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

   10. Simplified 60.8%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1200000000 \lor \neg \left(z \leq 8 \cdot 10^{+128}\right):\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+53}:\\ \;\;\;\;t + a \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+128}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.4e+53)
   (+ t (* a (/ t z)))
   (if (<= z 9e+128) (+ x (* t (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e+53) {
		tmp = t + (a * (t / z));
	} else if (z <= 9e+128) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.4d+53)) then
        tmp = t + (a * (t / z))
    else if (z <= 9d+128) then
        tmp = x + (t * (y / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e+53) {
		tmp = t + (a * (t / z));
	} else if (z <= 9e+128) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.4e+53:
		tmp = t + (a * (t / z))
	elif z <= 9e+128:
		tmp = x + (t * (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.4e+53)
		tmp = Float64(t + Float64(a * Float64(t / z)));
	elseif (z <= 9e+128)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.4e+53)
		tmp = t + (a * (t / z));
	elseif (z <= 9e+128)
		tmp = x + (t * (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.4e+53], N[(t + N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+128], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 3 regimes

2. if z < -5.40000000000000039e53

   1. Initial program 33.6%

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

      1. +-commutative 33.6%

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

      2. *-commutative 33.6%

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

      3. associate-/l* 66.9%

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

      4. fma-define 66.9%

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

   3. Simplified 66.9%

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

   5. Taylor expanded in y around 0 21.1%

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

      1. mul-1-neg 21.1%

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

      2. associate-/l* 44.9%

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

      3. distribute-lft-neg-out 44.9%

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

      4. +-commutative 44.9%

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

      5. *-commutative 44.9%

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

      6. fma-define 45.0%

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

   7. Simplified 45.0%

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

   8. Taylor expanded in z around -inf 48.7%

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

      1. mul-1-neg 48.7%

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

      2. unsub-neg 48.7%

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

      3. distribute-lft-out-- 49.3%

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

   10. Simplified 49.3%

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

   11. Taylor expanded in x around 0 43.2%

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

       1. sub-neg 43.2%

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

       2. mul-1-neg 43.2%

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

       3. remove-double-neg 43.2%

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

       4. associate-/l* 46.2%

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

   13. Simplified 46.2%

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

   if -5.40000000000000039e53 < z < 9.0000000000000003e128

   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* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in t around inf 70.7%

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

      1. associate-/l* 72.8%

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

   7. Simplified 72.8%

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

   8. Taylor expanded in z around 0 55.5%

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

      1. associate-/l* 59.0%

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

   10. Simplified 59.0%

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

   if 9.0000000000000003e128 < z

   1. Initial program 37.7%

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

      1. +-commutative 37.7%

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

      2. *-commutative 37.7%

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

      3. associate-/l* 73.7%

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

      4. fma-define 73.5%

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

   3. Simplified 73.5%

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

      1. add-cube-cbrt 72.2%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}, \frac{y - z}{a - z}, x\right) \]

      2. pow3 72.1%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   6. Applied egg-rr 72.1%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   7. Taylor expanded in z around inf 49.7%

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

Alternative 16: 36.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+68}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e-39) x (if (<= a 2.6e+68) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e-39) {
		tmp = x;
	} else if (a <= 2.6e+68) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9.5d-39)) then
        tmp = x
    else if (a <= 2.6d+68) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e-39) {
		tmp = x;
	} else if (a <= 2.6e+68) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e-39:
		tmp = x
	elif a <= 2.6e+68:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e-39)
		tmp = x;
	elseif (a <= 2.6e+68)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.5e-39)
		tmp = x;
	elseif (a <= 2.6e+68)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e-39], x, If[LessEqual[a, 2.6e+68], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -9.4999999999999999e-39 or 2.5999999999999998e68 < a

   1. Initial program 74.6%

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

      1. +-commutative 74.6%

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

      2. *-commutative 74.6%

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

      3. associate-/l* 91.5%

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

      4. fma-define 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in a around inf 47.5%

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

   if -9.4999999999999999e-39 < a < 2.5999999999999998e68

   1. Initial program 71.9%

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

      1. +-commutative 71.9%

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

      2. *-commutative 71.9%

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

      3. associate-/l* 81.7%

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

      4. fma-define 81.7%

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

   3. Simplified 81.7%

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

      1. add-cube-cbrt 80.4%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}, \frac{y - z}{a - z}, x\right) \]

      2. pow3 80.5%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   6. Applied egg-rr 80.5%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

   7. Taylor expanded in z around inf 29.6%

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

Alternative 17: 25.0% 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 73.1%

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

   1. +-commutative 73.1%

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

   2. *-commutative 73.1%

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

   3. associate-/l* 86.3%

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

   4. fma-define 86.3%

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

3. Simplified 86.3%

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

   1. add-cube-cbrt 85.3%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}, \frac{y - z}{a - z}, x\right) \]

   2. pow3 85.3%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

6. Applied egg-rr 85.3%

   \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

7. Taylor expanded in z around inf 19.9%

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

Alternative 18: 2.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 73.1%

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

   1. +-commutative 73.1%

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

   2. *-commutative 73.1%

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

   3. associate-/l* 86.3%

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

   4. fma-define 86.3%

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

3. Simplified 86.3%

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

   1. add-cube-cbrt 85.3%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}, \frac{y - z}{a - z}, x\right) \]

   2. pow3 85.3%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

6. Applied egg-rr 85.3%

   \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{t - x}\right)}^{3}}, \frac{y - z}{a - z}, x\right) \]

7. Taylor expanded in t around 0 42.4%

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

   1. mul-1-neg 42.4%

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

   2. unsub-neg 42.4%

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

   3. associate-/l* 46.8%

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

9. Simplified 46.8%

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

10. Taylor expanded in z around inf 2.7%

    \[\leadsto x - x \cdot \color{blue}{1} \]

11. Taylor expanded in x around 0 2.7%

    \[\leadsto \color{blue}{0} \]
12. Add Preprocessing

Developer Target 1: 83.6% 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 2024170 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

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

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