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

Percentage Accurate: 68.6% → 91.1%

Time: 17.4s

Alternatives: 21

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+288}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-275}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -1e+288)
     t_1
     (if (<= t_2 -2e-275)
       t_2
       (if (<= t_2 0.0)
         (+ t (/ (* (- t x) (- a y)) z))
         (if (<= t_2 2e+290) 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 <= -1e+288) {
		tmp = t_1;
	} else if (t_2 <= -2e-275) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 2e+290) {
		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 <= (-1d+288)) then
        tmp = t_1
    else if (t_2 <= (-2d-275)) then
        tmp = t_2
    else if (t_2 <= 0.0d0) then
        tmp = t + (((t - x) * (a - y)) / z)
    else if (t_2 <= 2d+290) 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 <= -1e+288) {
		tmp = t_1;
	} else if (t_2 <= -2e-275) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 2e+290) {
		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 <= -1e+288:
		tmp = t_1
	elif t_2 <= -2e-275:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t + (((t - x) * (a - y)) / z)
	elif t_2 <= 2e+290:
		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 <= -1e+288)
		tmp = t_1;
	elseif (t_2 <= -2e-275)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (t_2 <= 2e+290)
		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 <= -1e+288)
		tmp = t_1;
	elseif (t_2 <= -2e-275)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (t_2 <= 2e+290)
		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, -1e+288], t$95$1, If[LessEqual[t$95$2, -2e-275], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+290], 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))) < -1e288 or 2.00000000000000012e290 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 42.8%

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

      1. associate-/l* 81.9%

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

   3. Simplified 81.9%

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

   if -1e288 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.99999999999999987e-275 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 2.00000000000000012e290

   1. Initial program 95.5%

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

   if -1.99999999999999987e-275 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 3.9%

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

      1. +-commutative 3.9%

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

      2. *-commutative 3.9%

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

      3. associate-/l* 3.9%

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

      4. fma-define 3.9%

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

   3. Simplified 3.9%

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

   5. Taylor expanded in z around inf 99.6%

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

      1. associate--l+ 99.6%

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

      2. associate-*r/ 99.6%

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

      3. associate-*r/ 99.6%

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

      4. mul-1-neg 99.6%

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

      5. div-sub 99.6%

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

      6. mul-1-neg 99.6%

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

      7. distribute-lft-out-- 99.6%

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

      8. associate-*r/ 99.6%

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

      9. mul-1-neg 99.6%

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

      10. unsub-neg 99.6%

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

      11. distribute-rgt-out-- 99.6%

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

   7. Simplified 99.6%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{+288}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -2 \cdot 10^{-275}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 2 \cdot 10^{+290}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-275}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;a \cdot \frac{t - x}{z} - \left(a \cdot \frac{\left(t - x\right) \cdot \left(y - a\right)}{{z}^{2}} + \left(\frac{y \cdot \left(t - x\right)}{z} - t\right)\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_1 -2e-275)
     (fma (- t x) (/ (- y z) (- a z)) x)
     (if (<= t_1 0.0)
       (-
        (* a (/ (- t x) z))
        (+
         (* a (/ (* (- t x) (- y a)) (pow z 2.0)))
         (- (/ (* y (- t x)) z) t)))
       (if (<= t_1 2e+290) t_1 (fma (- y z) (/ (- t x) (- a z)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_1 <= -2e-275) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else if (t_1 <= 0.0) {
		tmp = (a * ((t - x) / z)) - ((a * (((t - x) * (y - a)) / pow(z, 2.0))) + (((y * (t - x)) / z) - t));
	} else if (t_1 <= 2e+290) {
		tmp = t_1;
	} else {
		tmp = fma((y - z), ((t - x) / (a - z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_1 <= -2e-275)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(a * Float64(Float64(t - x) / z)) - Float64(Float64(a * Float64(Float64(Float64(t - x) * Float64(y - a)) / (z ^ 2.0))) + Float64(Float64(Float64(y * Float64(t - x)) / z) - t)));
	elseif (t_1 <= 2e+290)
		tmp = t_1;
	else
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x);
	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[LessEqual[t$95$1, -2e-275], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(a * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(N[(a * N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+290], t$95$1, N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.99999999999999987e-275

   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* 88.2%

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

      4. fma-define 88.2%

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

   3. Simplified 88.2%

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

   if -1.99999999999999987e-275 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 3.9%

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

      1. +-commutative 3.9%

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

      2. *-commutative 3.9%

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

      3. associate-/l* 3.9%

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

      4. fma-define 3.9%

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

   3. Simplified 3.9%

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

   5. Taylor expanded in z around inf 93.4%

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

      1. sub-neg 93.4%

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

   7. Simplified 99.9%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 2.00000000000000012e290

   1. Initial program 95.1%

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

   if 2.00000000000000012e290 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 39.5%

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

      1. +-commutative 39.5%

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

      2. associate-/l* 80.2%

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

      3. fma-define 80.6%

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

   3. Simplified 80.6%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -2 \cdot 10^{-275}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;a \cdot \frac{t - x}{z} - \left(a \cdot \frac{\left(t - x\right) \cdot \left(y - a\right)}{{z}^{2}} + \left(\frac{y \cdot \left(t - x\right)}{z} - t\right)\right)\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 2 \cdot 10^{+290}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-275}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_1 -2e-275)
     (fma (- t x) (/ (- y z) (- a z)) x)
     (if (<= t_1 0.0)
       (+ t (/ (* (- t x) (- a y)) z))
       (if (<= t_1 2e+290) t_1 (fma (- y z) (/ (- t x) (- a z)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_1 <= -2e-275) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_1 <= 2e+290) {
		tmp = t_1;
	} else {
		tmp = fma((y - z), ((t - x) / (a - z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_1 <= -2e-275)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (t_1 <= 2e+290)
		tmp = t_1;
	else
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x);
	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[LessEqual[t$95$1, -2e-275], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+290], t$95$1, N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.99999999999999987e-275

   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* 88.2%

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

      4. fma-define 88.2%

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

   3. Simplified 88.2%

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

   if -1.99999999999999987e-275 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 3.9%

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

      1. +-commutative 3.9%

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

      2. *-commutative 3.9%

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

      3. associate-/l* 3.9%

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

      4. fma-define 3.9%

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

   3. Simplified 3.9%

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

   5. Taylor expanded in z around inf 99.6%

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

      1. associate--l+ 99.6%

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

      2. associate-*r/ 99.6%

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

      3. associate-*r/ 99.6%

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

      4. mul-1-neg 99.6%

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

      5. div-sub 99.6%

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

      6. mul-1-neg 99.6%

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

      7. distribute-lft-out-- 99.6%

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

      8. associate-*r/ 99.6%

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

      9. mul-1-neg 99.6%

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

      10. unsub-neg 99.6%

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

      11. distribute-rgt-out-- 99.6%

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

   7. Simplified 99.6%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 2.00000000000000012e290

   1. Initial program 95.1%

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

   if 2.00000000000000012e290 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 39.5%

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

      1. +-commutative 39.5%

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

      2. associate-/l* 80.2%

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

      3. fma-define 80.6%

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

   3. Simplified 80.6%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -2 \cdot 10^{-275}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 2 \cdot 10^{+290}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-275}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_1 -2e-275)
     (fma (- t x) (/ (- y z) (- a z)) x)
     (if (<= t_1 0.0)
       (+ t (/ (* (- t x) (- a y)) z))
       (if (<= t_1 2e+290) t_1 (+ x (* (- y z) (/ (- t x) (- 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 <= -2e-275) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_1 <= 2e+290) {
		tmp = t_1;
	} else {
		tmp = x + ((y - z) * ((t - x) / (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 <= -2e-275)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (t_1 <= 2e+290)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(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[LessEqual[t$95$1, -2e-275], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+290], t$95$1, N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.99999999999999987e-275

   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* 88.2%

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

      4. fma-define 88.2%

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

   3. Simplified 88.2%

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

   if -1.99999999999999987e-275 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 3.9%

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

      1. +-commutative 3.9%

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

      2. *-commutative 3.9%

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

      3. associate-/l* 3.9%

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

      4. fma-define 3.9%

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

   3. Simplified 3.9%

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

   5. Taylor expanded in z around inf 99.6%

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

      1. associate--l+ 99.6%

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

      2. associate-*r/ 99.6%

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

      3. associate-*r/ 99.6%

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

      4. mul-1-neg 99.6%

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

      5. div-sub 99.6%

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

      6. mul-1-neg 99.6%

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

      7. distribute-lft-out-- 99.6%

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

      8. associate-*r/ 99.6%

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

      9. mul-1-neg 99.6%

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

      10. unsub-neg 99.6%

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

      11. distribute-rgt-out-- 99.6%

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

   7. Simplified 99.6%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 2.00000000000000012e290

   1. Initial program 95.1%

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

   if 2.00000000000000012e290 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 39.5%

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

      1. associate-/l* 80.2%

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

   3. Simplified 80.2%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -2 \cdot 10^{-275}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 2 \cdot 10^{+290}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 47.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+170}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + 1\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-118}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1550000000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5e+170)
   t
   (if (<= z -4.2e-23)
     (* x (+ (/ y z) 1.0))
     (if (<= z -2.1e-118)
       (* t (/ y (- a z)))
       (if (<= z 1550000000.0) (* x (- 1.0 (/ y a))) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5e+170) {
		tmp = t;
	} else if (z <= -4.2e-23) {
		tmp = x * ((y / z) + 1.0);
	} else if (z <= -2.1e-118) {
		tmp = t * (y / (a - z));
	} else if (z <= 1550000000.0) {
		tmp = x * (1.0 - (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 <= (-5d+170)) then
        tmp = t
    else if (z <= (-4.2d-23)) then
        tmp = x * ((y / z) + 1.0d0)
    else if (z <= (-2.1d-118)) then
        tmp = t * (y / (a - z))
    else if (z <= 1550000000.0d0) then
        tmp = x * (1.0d0 - (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 <= -5e+170) {
		tmp = t;
	} else if (z <= -4.2e-23) {
		tmp = x * ((y / z) + 1.0);
	} else if (z <= -2.1e-118) {
		tmp = t * (y / (a - z));
	} else if (z <= 1550000000.0) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5e+170:
		tmp = t
	elif z <= -4.2e-23:
		tmp = x * ((y / z) + 1.0)
	elif z <= -2.1e-118:
		tmp = t * (y / (a - z))
	elif z <= 1550000000.0:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5e+170)
		tmp = t;
	elseif (z <= -4.2e-23)
		tmp = Float64(x * Float64(Float64(y / z) + 1.0));
	elseif (z <= -2.1e-118)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 1550000000.0)
		tmp = Float64(x * Float64(1.0 - 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 <= -5e+170)
		tmp = t;
	elseif (z <= -4.2e-23)
		tmp = x * ((y / z) + 1.0);
	elseif (z <= -2.1e-118)
		tmp = t * (y / (a - z));
	elseif (z <= 1550000000.0)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5e+170], t, If[LessEqual[z, -4.2e-23], N[(x * N[(N[(y / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.1e-118], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1550000000.0], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.99999999999999977e170 or 1.55e9 < z

   1. Initial program 37.0%

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

      1. associate-/l* 64.1%

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

   3. Simplified 64.1%

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

   5. Taylor expanded in t around inf 33.1%

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

      1. associate-/l* 61.2%

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

   7. Simplified 61.2%

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

   8. Taylor expanded in z around inf 47.4%

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

   9. Taylor expanded in x around 0 57.9%

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

   if -4.99999999999999977e170 < z < -4.2000000000000002e-23

   1. Initial program 72.8%

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

   5. Taylor expanded in y around inf 49.2%

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

      1. associate-*r/ 58.0%

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

   7. Simplified 58.0%

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

   8. Taylor expanded in x around inf 48.7%

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

      1. associate-*r/ 48.7%

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

      2. neg-mul-1 48.7%

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

   10. Simplified 48.7%

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

   11. Taylor expanded in a around 0 48.7%

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

       1. *-commutative 48.7%

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

   13. Simplified 48.7%

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

   if -4.2000000000000002e-23 < z < -2.1e-118

   1. Initial program 88.0%

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

      1. +-commutative 88.0%

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

      2. *-commutative 88.0%

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

      3. associate-/l* 79.9%

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

      4. fma-define 80.0%

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

   3. Simplified 80.0%

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

   5. Taylor expanded in t around inf 59.9%

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

   6. Taylor expanded in y around inf 51.6%

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

   if -2.1e-118 < z < 1.55e9

   1. Initial program 89.9%

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

      1. associate-/l* 86.8%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in y around inf 82.1%

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

      1. associate-*r/ 80.7%

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

   7. Simplified 80.7%

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

   8. Taylor expanded in x around inf 58.6%

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

      1. associate-*r/ 58.6%

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

      2. neg-mul-1 58.6%

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

   10. Simplified 58.6%

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

   11. Taylor expanded in a around inf 50.9%

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

       1. *-rgt-identity 50.9%

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

       2. mul-1-neg 50.9%

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

       3. associate-/l* 54.1%

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

       4. distribute-rgt-neg-in 54.1%

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

       5. mul-1-neg 54.1%

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

       6. distribute-lft-in 54.1%

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

       7. *-commutative 54.1%

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

       8. mul-1-neg 54.1%

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

       9. unsub-neg 54.1%

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

   13. Simplified 54.1%

       \[\leadsto \color{blue}{\left(1 - \frac{y}{a}\right) \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+170}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + 1\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-118}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1550000000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 38.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} + 1\right)\\ \mathbf{if}\;z \leq -5 \cdot 10^{+170}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-198}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2150000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (+ (/ y z) 1.0))))
   (if (<= z -5e+170)
     t
     (if (<= z -7.2e-23)
       t_1
       (if (<= z 2.45e-198)
         (* t (/ y (- a z)))
         (if (<= z 2150000000.0) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y / z) + 1.0);
	double tmp;
	if (z <= -5e+170) {
		tmp = t;
	} else if (z <= -7.2e-23) {
		tmp = t_1;
	} else if (z <= 2.45e-198) {
		tmp = t * (y / (a - z));
	} else if (z <= 2150000000.0) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y / z) + 1.0d0)
    if (z <= (-5d+170)) then
        tmp = t
    else if (z <= (-7.2d-23)) then
        tmp = t_1
    else if (z <= 2.45d-198) then
        tmp = t * (y / (a - z))
    else if (z <= 2150000000.0d0) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y / z) + 1.0);
	double tmp;
	if (z <= -5e+170) {
		tmp = t;
	} else if (z <= -7.2e-23) {
		tmp = t_1;
	} else if (z <= 2.45e-198) {
		tmp = t * (y / (a - z));
	} else if (z <= 2150000000.0) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y / z) + 1.0)
	tmp = 0
	if z <= -5e+170:
		tmp = t
	elif z <= -7.2e-23:
		tmp = t_1
	elif z <= 2.45e-198:
		tmp = t * (y / (a - z))
	elif z <= 2150000000.0:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y / z) + 1.0))
	tmp = 0.0
	if (z <= -5e+170)
		tmp = t;
	elseif (z <= -7.2e-23)
		tmp = t_1;
	elseif (z <= 2.45e-198)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 2150000000.0)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y / z) + 1.0);
	tmp = 0.0;
	if (z <= -5e+170)
		tmp = t;
	elseif (z <= -7.2e-23)
		tmp = t_1;
	elseif (z <= 2.45e-198)
		tmp = t * (y / (a - z));
	elseif (z <= 2150000000.0)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+170], t, If[LessEqual[z, -7.2e-23], t$95$1, If[LessEqual[z, 2.45e-198], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2150000000.0], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.99999999999999977e170 or 2.15e9 < z

   1. Initial program 37.0%

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

      1. associate-/l* 64.1%

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

   3. Simplified 64.1%

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

   5. Taylor expanded in t around inf 33.1%

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

      1. associate-/l* 61.2%

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

   7. Simplified 61.2%

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

   8. Taylor expanded in z around inf 47.4%

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

   9. Taylor expanded in x around 0 57.9%

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

   if -4.99999999999999977e170 < z < -7.1999999999999996e-23 or 2.4500000000000001e-198 < z < 2.15e9

   1. Initial program 79.8%

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

      1. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in y around inf 62.7%

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

      1. associate-*r/ 69.1%

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

   7. Simplified 69.1%

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

   8. Taylor expanded in x around inf 54.1%

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

      1. associate-*r/ 54.1%

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

      2. neg-mul-1 54.1%

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

   10. Simplified 54.1%

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

   11. Taylor expanded in a around 0 43.5%

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

       1. *-commutative 43.5%

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

   13. Simplified 43.5%

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

   if -7.1999999999999996e-23 < z < 2.4500000000000001e-198

   1. Initial program 91.6%

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

      1. +-commutative 91.6%

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

      2. *-commutative 91.6%

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

      3. associate-/l* 89.4%

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

      4. fma-define 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in t around inf 45.4%

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

   6. Taylor expanded in y around inf 40.0%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+170}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + 1\right)\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-198}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2150000000:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+165}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-113}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (* (- t x) (- a y)) z))))
   (if (<= z -6.2e+165)
     t_1
     (if (<= z -1.75e-113)
       (+ x (* (- y z) (/ t (- a z))))
       (if (<= z 5.2e-87) (+ x (/ (* y (- t x)) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) * (a - y)) / z);
	double tmp;
	if (z <= -6.2e+165) {
		tmp = t_1;
	} else if (z <= -1.75e-113) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else if (z <= 5.2e-87) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (((t - x) * (a - y)) / z)
    if (z <= (-6.2d+165)) then
        tmp = t_1
    else if (z <= (-1.75d-113)) then
        tmp = x + ((y - z) * (t / (a - z)))
    else if (z <= 5.2d-87) then
        tmp = x + ((y * (t - x)) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) * (a - y)) / z);
	double tmp;
	if (z <= -6.2e+165) {
		tmp = t_1;
	} else if (z <= -1.75e-113) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else if (z <= 5.2e-87) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (((t - x) * (a - y)) / z)
	tmp = 0
	if z <= -6.2e+165:
		tmp = t_1
	elif z <= -1.75e-113:
		tmp = x + ((y - z) * (t / (a - z)))
	elif z <= 5.2e-87:
		tmp = x + ((y * (t - x)) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z))
	tmp = 0.0
	if (z <= -6.2e+165)
		tmp = t_1;
	elseif (z <= -1.75e-113)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	elseif (z <= 5.2e-87)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (((t - x) * (a - y)) / z);
	tmp = 0.0;
	if (z <= -6.2e+165)
		tmp = t_1;
	elseif (z <= -1.75e-113)
		tmp = x + ((y - z) * (t / (a - z)));
	elseif (z <= 5.2e-87)
		tmp = x + ((y * (t - x)) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e+165], t$95$1, If[LessEqual[z, -1.75e-113], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-87], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.2000000000000003e165 or 5.20000000000000005e-87 < z

   1. Initial program 44.9%

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

      1. +-commutative 44.9%

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

      2. *-commutative 44.9%

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

      3. associate-/l* 69.9%

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

      4. fma-define 69.9%

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

   3. Simplified 69.9%

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

   5. Taylor expanded in z around inf 73.7%

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

      1. associate--l+ 73.7%

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

      2. associate-*r/ 73.7%

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

      3. associate-*r/ 73.7%

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

      4. mul-1-neg 73.7%

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

      5. div-sub 73.7%

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

      6. mul-1-neg 73.7%

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

      7. distribute-lft-out-- 73.7%

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

      8. associate-*r/ 73.7%

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

      9. mul-1-neg 73.7%

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

      10. unsub-neg 73.7%

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

      11. distribute-rgt-out-- 73.7%

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

   7. Simplified 73.7%

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

   if -6.2000000000000003e165 < z < -1.75000000000000014e-113

   1. Initial program 78.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 74.5%

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

   if -1.75000000000000014e-113 < z < 5.20000000000000005e-87

   1. Initial program 91.8%

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

   3. Taylor expanded in y around inf 87.0%

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

      1. *-commutative 87.0%

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

   5. Simplified 87.0%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+165}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-113}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+128}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-126}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-66}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.3e+128)
   (* t (/ z (- z a)))
   (if (<= z -4.8e-126)
     (+ x (/ y (/ (- a z) t)))
     (if (<= z 1.85e-66)
       (+ x (/ (* y (- t x)) a))
       (- x (* t (/ z (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+128) {
		tmp = t * (z / (z - a));
	} else if (z <= -4.8e-126) {
		tmp = x + (y / ((a - z) / t));
	} else if (z <= 1.85e-66) {
		tmp = x + ((y * (t - x)) / a);
	} else {
		tmp = x - (t * (z / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.3d+128)) then
        tmp = t * (z / (z - a))
    else if (z <= (-4.8d-126)) then
        tmp = x + (y / ((a - z) / t))
    else if (z <= 1.85d-66) then
        tmp = x + ((y * (t - x)) / a)
    else
        tmp = x - (t * (z / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+128) {
		tmp = t * (z / (z - a));
	} else if (z <= -4.8e-126) {
		tmp = x + (y / ((a - z) / t));
	} else if (z <= 1.85e-66) {
		tmp = x + ((y * (t - x)) / a);
	} else {
		tmp = x - (t * (z / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.3e+128:
		tmp = t * (z / (z - a))
	elif z <= -4.8e-126:
		tmp = x + (y / ((a - z) / t))
	elif z <= 1.85e-66:
		tmp = x + ((y * (t - x)) / a)
	else:
		tmp = x - (t * (z / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.3e+128)
		tmp = Float64(t * Float64(z / Float64(z - a)));
	elseif (z <= -4.8e-126)
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	elseif (z <= 1.85e-66)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	else
		tmp = Float64(x - Float64(t * Float64(z / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.3e+128)
		tmp = t * (z / (z - a));
	elseif (z <= -4.8e-126)
		tmp = x + (y / ((a - z) / t));
	elseif (z <= 1.85e-66)
		tmp = x + ((y * (t - x)) / a);
	else
		tmp = x - (t * (z / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.3e+128], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.8e-126], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e-66], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.3e128

   1. Initial program 29.9%

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

      1. +-commutative 29.9%

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

      2. *-commutative 29.9%

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

      3. associate-/l* 63.0%

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

      4. fma-define 63.0%

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

   3. Simplified 63.0%

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

   5. Taylor expanded in t around inf 68.7%

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

   6. Taylor expanded in y around 0 66.3%

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

      1. neg-mul-1 66.3%

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

      2. distribute-neg-frac 66.3%

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

   8. Simplified 66.3%

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

   if -1.3e128 < z < -4.80000000000000014e-126

   1. Initial program 85.8%

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

      1. associate-/l* 90.0%

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

   3. Simplified 90.0%

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

      1. clear-num 89.9%

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

      2. un-div-inv 89.8%

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

   6. Applied egg-rr 89.8%

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

   7. Taylor expanded in t around inf 80.0%

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

   8. Taylor expanded in y around inf 60.0%

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

   if -4.80000000000000014e-126 < z < 1.8500000000000001e-66

   1. Initial program 91.8%

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

      1. associate-/l* 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in z around 0 75.9%

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

   if 1.8500000000000001e-66 < z

   1. Initial program 48.0%

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

      1. associate-/l* 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in t around inf 41.2%

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

      1. associate-/l* 63.7%

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

   7. Simplified 63.7%

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

   8. Taylor expanded in y around 0 33.5%

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

      1. mul-1-neg 33.5%

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

      2. unsub-neg 33.5%

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

      3. associate-/l* 54.8%

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

   10. Simplified 54.8%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+128}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-126}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-66}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+127}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-118}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3e+127)
   (* t (/ z (- z a)))
   (if (<= z -1.8e-118)
     (+ x (/ y (/ (- a z) t)))
     (if (<= z 5.2e-87) (+ x (/ (* y (- t x)) a)) (* t (- 1.0 (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e+127) {
		tmp = t * (z / (z - a));
	} else if (z <= -1.8e-118) {
		tmp = x + (y / ((a - z) / t));
	} else if (z <= 5.2e-87) {
		tmp = x + ((y * (t - x)) / a);
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3d+127)) then
        tmp = t * (z / (z - a))
    else if (z <= (-1.8d-118)) then
        tmp = x + (y / ((a - z) / t))
    else if (z <= 5.2d-87) then
        tmp = x + ((y * (t - x)) / a)
    else
        tmp = t * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e+127) {
		tmp = t * (z / (z - a));
	} else if (z <= -1.8e-118) {
		tmp = x + (y / ((a - z) / t));
	} else if (z <= 5.2e-87) {
		tmp = x + ((y * (t - x)) / a);
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3e+127:
		tmp = t * (z / (z - a))
	elif z <= -1.8e-118:
		tmp = x + (y / ((a - z) / t))
	elif z <= 5.2e-87:
		tmp = x + ((y * (t - x)) / a)
	else:
		tmp = t * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3e+127)
		tmp = Float64(t * Float64(z / Float64(z - a)));
	elseif (z <= -1.8e-118)
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	elseif (z <= 5.2e-87)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	else
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3e+127)
		tmp = t * (z / (z - a));
	elseif (z <= -1.8e-118)
		tmp = x + (y / ((a - z) / t));
	elseif (z <= 5.2e-87)
		tmp = x + ((y * (t - x)) / a);
	else
		tmp = t * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3e+127], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.8e-118], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-87], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.0000000000000002e127

   1. Initial program 29.9%

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

      1. +-commutative 29.9%

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

      2. *-commutative 29.9%

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

      3. associate-/l* 63.0%

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

      4. fma-define 63.0%

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

   3. Simplified 63.0%

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

   5. Taylor expanded in t around inf 68.7%

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

   6. Taylor expanded in y around 0 66.3%

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

      1. neg-mul-1 66.3%

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

      2. distribute-neg-frac 66.3%

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

   8. Simplified 66.3%

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

   if -3.0000000000000002e127 < z < -1.8000000000000001e-118

   1. Initial program 85.8%

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

      1. associate-/l* 90.0%

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

   3. Simplified 90.0%

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

      1. clear-num 89.9%

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

      2. un-div-inv 89.8%

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

   6. Applied egg-rr 89.8%

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

   7. Taylor expanded in t around inf 80.0%

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

   8. Taylor expanded in y around inf 60.0%

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

   if -1.8000000000000001e-118 < z < 5.20000000000000005e-87

   1. Initial program 91.6%

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

      1. associate-/l* 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in z around 0 77.3%

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

   if 5.20000000000000005e-87 < z

   1. Initial program 49.9%

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

      1. +-commutative 49.9%

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

      2. *-commutative 49.9%

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

      3. associate-/l* 74.1%

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

      4. fma-define 74.1%

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

   3. Simplified 74.1%

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

   5. Taylor expanded in t around inf 61.0%

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

   6. Taylor expanded in a around 0 53.6%

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

      1. associate-*r/ 53.6%

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

      2. neg-mul-1 53.6%

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

   8. Simplified 53.6%

      \[\leadsto \color{blue}{t \cdot \left(1 + \frac{-y}{z}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+127}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-118}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+127}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-118}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-87}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.6e+127)
   (* t (/ z (- z a)))
   (if (<= z -3.6e-118)
     (+ x (/ y (/ (- a z) t)))
     (if (<= z 5.2e-87) (+ x (* y (/ (- t x) a))) (* t (- 1.0 (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e+127) {
		tmp = t * (z / (z - a));
	} else if (z <= -3.6e-118) {
		tmp = x + (y / ((a - z) / t));
	} else if (z <= 5.2e-87) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.6d+127)) then
        tmp = t * (z / (z - a))
    else if (z <= (-3.6d-118)) then
        tmp = x + (y / ((a - z) / t))
    else if (z <= 5.2d-87) then
        tmp = x + (y * ((t - x) / a))
    else
        tmp = t * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e+127) {
		tmp = t * (z / (z - a));
	} else if (z <= -3.6e-118) {
		tmp = x + (y / ((a - z) / t));
	} else if (z <= 5.2e-87) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.6e+127:
		tmp = t * (z / (z - a))
	elif z <= -3.6e-118:
		tmp = x + (y / ((a - z) / t))
	elif z <= 5.2e-87:
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = t * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.6e+127)
		tmp = Float64(t * Float64(z / Float64(z - a)));
	elseif (z <= -3.6e-118)
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	elseif (z <= 5.2e-87)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	else
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.6e+127)
		tmp = t * (z / (z - a));
	elseif (z <= -3.6e-118)
		tmp = x + (y / ((a - z) / t));
	elseif (z <= 5.2e-87)
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.6e+127], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.6e-118], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-87], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.6000000000000002e127

   1. Initial program 29.9%

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

      1. +-commutative 29.9%

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

      2. *-commutative 29.9%

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

      3. associate-/l* 63.0%

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

      4. fma-define 63.0%

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

   3. Simplified 63.0%

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

   5. Taylor expanded in t around inf 68.7%

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

   6. Taylor expanded in y around 0 66.3%

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

      1. neg-mul-1 66.3%

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

      2. distribute-neg-frac 66.3%

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

   8. Simplified 66.3%

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

   if -2.6000000000000002e127 < z < -3.6000000000000002e-118

   1. Initial program 85.8%

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

      1. associate-/l* 90.0%

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

   3. Simplified 90.0%

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

      1. clear-num 89.9%

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

      2. un-div-inv 89.8%

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

   6. Applied egg-rr 89.8%

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

   7. Taylor expanded in t around inf 80.0%

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

   8. Taylor expanded in y around inf 60.0%

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

   if -3.6000000000000002e-118 < z < 5.20000000000000005e-87

   1. Initial program 91.6%

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

      1. associate-/l* 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in z around 0 77.3%

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

      1. associate-/l* 76.7%

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

   7. Simplified 76.7%

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

   if 5.20000000000000005e-87 < z

   1. Initial program 49.9%

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

      1. +-commutative 49.9%

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

      2. *-commutative 49.9%

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

      3. associate-/l* 74.1%

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

      4. fma-define 74.1%

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

   3. Simplified 74.1%

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

   5. Taylor expanded in t around inf 61.0%

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

   6. Taylor expanded in a around 0 53.6%

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

      1. associate-*r/ 53.6%

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

      2. neg-mul-1 53.6%

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

   8. Simplified 53.6%

      \[\leadsto \color{blue}{t \cdot \left(1 + \frac{-y}{z}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+127}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-118}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-87}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+127}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-124}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-87}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e+127)
   (* t (/ z (- z a)))
   (if (<= z -3.5e-124)
     (+ x (* y (/ t (- a z))))
     (if (<= z 5.2e-87) (+ x (* y (/ (- t x) a))) (* t (- 1.0 (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+127) {
		tmp = t * (z / (z - a));
	} else if (z <= -3.5e-124) {
		tmp = x + (y * (t / (a - z)));
	} else if (z <= 5.2e-87) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.8d+127)) then
        tmp = t * (z / (z - a))
    else if (z <= (-3.5d-124)) then
        tmp = x + (y * (t / (a - z)))
    else if (z <= 5.2d-87) then
        tmp = x + (y * ((t - x) / a))
    else
        tmp = t * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+127) {
		tmp = t * (z / (z - a));
	} else if (z <= -3.5e-124) {
		tmp = x + (y * (t / (a - z)));
	} else if (z <= 5.2e-87) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.8e+127:
		tmp = t * (z / (z - a))
	elif z <= -3.5e-124:
		tmp = x + (y * (t / (a - z)))
	elif z <= 5.2e-87:
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = t * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e+127)
		tmp = Float64(t * Float64(z / Float64(z - a)));
	elseif (z <= -3.5e-124)
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	elseif (z <= 5.2e-87)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	else
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.8e+127)
		tmp = t * (z / (z - a));
	elseif (z <= -3.5e-124)
		tmp = x + (y * (t / (a - z)));
	elseif (z <= 5.2e-87)
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e+127], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.5e-124], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-87], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.79999999999999989e127

   1. Initial program 29.9%

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

      1. +-commutative 29.9%

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

      2. *-commutative 29.9%

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

      3. associate-/l* 63.0%

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

      4. fma-define 63.0%

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

   3. Simplified 63.0%

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

   5. Taylor expanded in t around inf 68.7%

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

   6. Taylor expanded in y around 0 66.3%

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

      1. neg-mul-1 66.3%

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

      2. distribute-neg-frac 66.3%

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

   8. Simplified 66.3%

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

   if -1.79999999999999989e127 < z < -3.4999999999999999e-124

   1. Initial program 85.8%

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

   3. Taylor expanded in t around inf 76.0%

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

   4. Taylor expanded in y around inf 56.0%

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

   5. Taylor expanded in y around 0 56.0%

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

      1. *-commutative 56.0%

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

      2. associate-*r/ 59.9%

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

   7. Simplified 59.9%

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

   if -3.4999999999999999e-124 < z < 5.20000000000000005e-87

   1. Initial program 91.6%

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

      1. associate-/l* 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in z around 0 77.3%

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

      1. associate-/l* 76.7%

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

   7. Simplified 76.7%

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

   if 5.20000000000000005e-87 < z

   1. Initial program 49.9%

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

      1. +-commutative 49.9%

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

      2. *-commutative 49.9%

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

      3. associate-/l* 74.1%

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

      4. fma-define 74.1%

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

   3. Simplified 74.1%

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

   5. Taylor expanded in t around inf 61.0%

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

   6. Taylor expanded in a around 0 53.6%

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

      1. associate-*r/ 53.6%

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

      2. neg-mul-1 53.6%

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

   8. Simplified 53.6%

      \[\leadsto \color{blue}{t \cdot \left(1 + \frac{-y}{z}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+127}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-124}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-87}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 83.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-162} \lor \neg \left(a \leq 5.1 \cdot 10^{-144}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3e-162) (not (<= a 5.1e-144)))
   (+ x (* (- y z) (/ (- t x) (- a z))))
   (+ t (/ (* (- t x) (- a y)) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3e-162) || !(a <= 5.1e-144)) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3d-162)) .or. (.not. (a <= 5.1d-144))) then
        tmp = x + ((y - z) * ((t - x) / (a - z)))
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3e-162) || !(a <= 5.1e-144)) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3e-162) or not (a <= 5.1e-144):
		tmp = x + ((y - z) * ((t - x) / (a - z)))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3e-162) || !(a <= 5.1e-144))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3e-162) || ~((a <= 5.1e-144)))
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3e-162], N[Not[LessEqual[a, 5.1e-144]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.99999999999999999e-162 or 5.1e-144 < a

   1. Initial program 69.4%

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

      1. associate-/l* 81.7%

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

   3. Simplified 81.7%

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

   if -2.99999999999999999e-162 < a < 5.1e-144

   1. Initial program 66.9%

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

      1. +-commutative 66.9%

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

      2. *-commutative 66.9%

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

      3. associate-/l* 79.6%

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

      4. fma-define 79.6%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in z around inf 88.5%

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

      1. associate--l+ 88.5%

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

      2. associate-*r/ 88.5%

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

      3. associate-*r/ 88.5%

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

      4. mul-1-neg 88.5%

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

      5. div-sub 90.2%

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

      6. mul-1-neg 90.2%

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

      7. distribute-lft-out-- 90.2%

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

      8. associate-*r/ 90.2%

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

      9. mul-1-neg 90.2%

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

      10. unsub-neg 90.2%

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

      11. distribute-rgt-out-- 90.2%

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

   7. Simplified 90.2%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-162} \lor \neg \left(a \leq 5.1 \cdot 10^{-144}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+94} \lor \neg \left(y \leq 2.45 \cdot 10^{+27}\right):\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y - z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.4e+94) (not (<= y 2.45e+27)))
   (+ x (* y (/ (- t x) (- a z))))
   (- x (* t (/ (- y z) (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.4e+94) || !(y <= 2.45e+27)) {
		tmp = x + (y * ((t - x) / (a - z)));
	} else {
		tmp = x - (t * ((y - z) / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-2.4d+94)) .or. (.not. (y <= 2.45d+27))) then
        tmp = x + (y * ((t - x) / (a - z)))
    else
        tmp = x - (t * ((y - z) / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.4e+94) || !(y <= 2.45e+27)) {
		tmp = x + (y * ((t - x) / (a - z)));
	} else {
		tmp = x - (t * ((y - z) / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.4e+94) or not (y <= 2.45e+27):
		tmp = x + (y * ((t - x) / (a - z)))
	else:
		tmp = x - (t * ((y - z) / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.4e+94) || !(y <= 2.45e+27))
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / Float64(a - z))));
	else
		tmp = Float64(x - Float64(t * Float64(Float64(y - z) / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.4e+94) || ~((y <= 2.45e+27)))
		tmp = x + (y * ((t - x) / (a - z)));
	else
		tmp = x - (t * ((y - z) / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.4e+94], N[Not[LessEqual[y, 2.45e+27]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.39999999999999983e94 or 2.45000000000000007e27 < y

   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* 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in y around inf 71.9%

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

      1. associate-*r/ 81.6%

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

   7. Simplified 81.6%

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

   if -2.39999999999999983e94 < y < 2.45000000000000007e27

   1. Initial program 65.6%

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

      1. associate-/l* 73.4%

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

   3. Simplified 73.4%

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

   5. Taylor expanded in t around inf 61.3%

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

      1. associate-/l* 72.7%

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

   7. Simplified 72.7%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+94} \lor \neg \left(y \leq 2.45 \cdot 10^{+27}\right):\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y - z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 72.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - z}{z - a}\\ \mathbf{if}\;t \leq -6.6 \cdot 10^{-102} \lor \neg \left(t \leq 4.2 \cdot 10^{-59}\right):\\ \;\;\;\;x - t \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t\_1 + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y z) (- z a))))
   (if (or (<= t -6.6e-102) (not (<= t 4.2e-59)))
     (- x (* t t_1))
     (* x (+ t_1 1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) / (z - a);
	double tmp;
	if ((t <= -6.6e-102) || !(t <= 4.2e-59)) {
		tmp = x - (t * t_1);
	} else {
		tmp = x * (t_1 + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) / (z - a)
    if ((t <= (-6.6d-102)) .or. (.not. (t <= 4.2d-59))) then
        tmp = x - (t * t_1)
    else
        tmp = x * (t_1 + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) / (z - a);
	double tmp;
	if ((t <= -6.6e-102) || !(t <= 4.2e-59)) {
		tmp = x - (t * t_1);
	} else {
		tmp = x * (t_1 + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) / (z - a)
	tmp = 0
	if (t <= -6.6e-102) or not (t <= 4.2e-59):
		tmp = x - (t * t_1)
	else:
		tmp = x * (t_1 + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) / Float64(z - a))
	tmp = 0.0
	if ((t <= -6.6e-102) || !(t <= 4.2e-59))
		tmp = Float64(x - Float64(t * t_1));
	else
		tmp = Float64(x * Float64(t_1 + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) / (z - a);
	tmp = 0.0;
	if ((t <= -6.6e-102) || ~((t <= 4.2e-59)))
		tmp = x - (t * t_1);
	else
		tmp = x * (t_1 + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -6.6e-102], N[Not[LessEqual[t, 4.2e-59]], $MachinePrecision]], N[(x - N[(t * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x * N[(t$95$1 + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.6e-102 or 4.19999999999999993e-59 < t

   1. Initial program 69.6%

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

      1. associate-/l* 87.2%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in t around inf 64.5%

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

      1. associate-/l* 82.3%

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

   7. Simplified 82.3%

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

   if -6.6e-102 < t < 4.19999999999999993e-59

   1. Initial program 67.3%

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

      1. +-commutative 67.3%

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

      2. *-commutative 67.3%

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

      3. associate-/l* 67.4%

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

      4. fma-define 67.4%

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

   3. Simplified 67.4%

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

   5. Taylor expanded in t around 0 55.3%

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

      1. *-rgt-identity 55.3%

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

      2. mul-1-neg 55.3%

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

      3. associate-/l* 57.0%

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

      4. distribute-rgt-neg-in 57.0%

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

      5. mul-1-neg 57.0%

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

      6. distribute-lft-in 57.0%

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

      7. mul-1-neg 57.0%

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

      8. unsub-neg 57.0%

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

   7. Simplified 57.0%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y - z}{a - z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-102} \lor \neg \left(t \leq 4.2 \cdot 10^{-59}\right):\\ \;\;\;\;x - t \cdot \frac{y - z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 58.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.4 \cdot 10^{-39} \lor \neg \left(a \leq 1.45\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -8.4e-39) (not (<= a 1.45)))
   (+ x (* t (/ (- y z) a)))
   (* t (- 1.0 (/ y z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.4e-39) || !(a <= 1.45)) {
		tmp = x + (t * ((y - z) / a));
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-8.4d-39)) .or. (.not. (a <= 1.45d0))) then
        tmp = x + (t * ((y - z) / a))
    else
        tmp = t * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.4e-39) || !(a <= 1.45)) {
		tmp = x + (t * ((y - z) / a));
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -8.4e-39) or not (a <= 1.45):
		tmp = x + (t * ((y - z) / a))
	else:
		tmp = t * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -8.4e-39) || !(a <= 1.45))
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / a)));
	else
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -8.4e-39) || ~((a <= 1.45)))
		tmp = x + (t * ((y - z) / a));
	else
		tmp = t * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -8.4e-39], N[Not[LessEqual[a, 1.45]], $MachinePrecision]], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.39999999999999973e-39 or 1.44999999999999996 < a

   1. Initial program 69.0%

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

      1. associate-/l* 85.0%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in t around inf 64.3%

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

      1. associate-/l* 76.0%

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

   7. Simplified 76.0%

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

   8. Taylor expanded in a around inf 60.0%

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

      1. associate-/l* 65.2%

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

   10. Simplified 65.2%

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

   if -8.39999999999999973e-39 < a < 1.44999999999999996

   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* 77.7%

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

      4. fma-define 77.8%

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

   3. Simplified 77.8%

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

   5. Taylor expanded in t around inf 62.0%

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

   6. Taylor expanded in a around 0 57.1%

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

      1. associate-*r/ 57.1%

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

      2. neg-mul-1 57.1%

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

   8. Simplified 57.1%

      \[\leadsto \color{blue}{t \cdot \left(1 + \frac{-y}{z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.4 \cdot 10^{-39} \lor \neg \left(a \leq 1.45\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 55.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-35} \lor \neg \left(a \leq 0.00365\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.6e-35) (not (<= a 0.00365)))
   (+ x (* t (/ y a)))
   (* t (- 1.0 (/ y z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.6e-35) || !(a <= 0.00365)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.6d-35)) .or. (.not. (a <= 0.00365d0))) then
        tmp = x + (t * (y / a))
    else
        tmp = t * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.6e-35) || !(a <= 0.00365)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.6e-35) or not (a <= 0.00365):
		tmp = x + (t * (y / a))
	else:
		tmp = t * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.6e-35) || !(a <= 0.00365))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.6e-35) || ~((a <= 0.00365)))
		tmp = x + (t * (y / a));
	else
		tmp = t * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.6e-35], N[Not[LessEqual[a, 0.00365]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.5999999999999999e-35 or 0.00365000000000000003 < a

   1. Initial program 69.0%

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

      1. associate-/l* 85.0%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in t around inf 64.3%

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

      1. associate-/l* 76.0%

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

   7. Simplified 76.0%

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

   8. Taylor expanded in z around 0 52.6%

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

      1. associate-/l* 55.8%

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

   10. Simplified 55.8%

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

   if -1.5999999999999999e-35 < a < 0.00365000000000000003

   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* 77.7%

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

      4. fma-define 77.8%

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

   3. Simplified 77.8%

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

   5. Taylor expanded in t around inf 62.0%

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

   6. Taylor expanded in a around 0 57.1%

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

      1. associate-*r/ 57.1%

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

      2. neg-mul-1 57.1%

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

   8. Simplified 57.1%

      \[\leadsto \color{blue}{t \cdot \left(1 + \frac{-y}{z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-35} \lor \neg \left(a \leq 0.00365\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 42.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+15} \lor \neg \left(y \leq 1.8 \cdot 10^{+118}\right):\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.3e+15) (not (<= y 1.8e+118))) (* t (/ y (- a z))) (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.3e+15) || !(y <= 1.8e+118)) {
		tmp = t * (y / (a - z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.3d+15)) .or. (.not. (y <= 1.8d+118))) then
        tmp = t * (y / (a - z))
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.3e+15) || !(y <= 1.8e+118)) {
		tmp = t * (y / (a - z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.3e+15) or not (y <= 1.8e+118):
		tmp = t * (y / (a - z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.3e+15) || !(y <= 1.8e+118))
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.3e+15) || ~((y <= 1.8e+118)))
		tmp = t * (y / (a - z));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.3e+15], N[Not[LessEqual[y, 1.8e+118]], $MachinePrecision]], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e15 or 1.8e118 < y

   1. Initial program 74.2%

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

      1. +-commutative 74.2%

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

      2. *-commutative 74.2%

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

      3. associate-/l* 87.4%

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

      4. fma-define 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in t around inf 54.9%

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

   6. Taylor expanded in y around inf 44.3%

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

   if -1.3e15 < y < 1.8e118

   1. Initial program 65.8%

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

      1. associate-/l* 72.9%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in t around inf 60.9%

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

      1. associate-/l* 71.3%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in z around inf 43.5%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+15} \lor \neg \left(y \leq 1.8 \cdot 10^{+118}\right):\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+127}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2700000000:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e+127) t (if (<= z 2700000000.0) (+ x (* t (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+127) {
		tmp = t;
	} else if (z <= 2700000000.0) {
		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 <= (-1.8d+127)) then
        tmp = t
    else if (z <= 2700000000.0d0) 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 <= -1.8e+127) {
		tmp = t;
	} else if (z <= 2700000000.0) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.8e+127:
		tmp = t
	elif z <= 2700000000.0:
		tmp = x + (t * (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e+127)
		tmp = t;
	elseif (z <= 2700000000.0)
		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 <= -1.8e+127)
		tmp = t;
	elseif (z <= 2700000000.0)
		tmp = x + (t * (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e+127], t, If[LessEqual[z, 2700000000.0], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.79999999999999989e127 or 2.7e9 < z

   1. Initial program 37.3%

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

      1. associate-/l* 65.0%

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

   3. Simplified 65.0%

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

   5. Taylor expanded in t around inf 32.6%

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

      1. associate-/l* 59.3%

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

   7. Simplified 59.3%

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

   8. Taylor expanded in z around inf 44.8%

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

   9. Taylor expanded in x around 0 54.5%

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

   if -1.79999999999999989e127 < z < 2.7e9

   1. Initial program 88.6%

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

   5. Taylor expanded in t around inf 68.5%

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

      1. associate-/l* 70.3%

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

   7. Simplified 70.3%

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

   8. Taylor expanded in z around 0 46.8%

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

      1. associate-/l* 51.5%

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

   10. Simplified 51.5%

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

Alternative 19: 39.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+72} \lor \neg \left(y \leq 3.4 \cdot 10^{+154}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4.8e+72) (not (<= y 3.4e+154))) (* t (/ y a)) (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.8e+72) || !(y <= 3.4e+154)) {
		tmp = t * (y / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-4.8d+72)) .or. (.not. (y <= 3.4d+154))) then
        tmp = t * (y / a)
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.8e+72) || !(y <= 3.4e+154)) {
		tmp = t * (y / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4.8e+72) or not (y <= 3.4e+154):
		tmp = t * (y / a)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4.8e+72) || !(y <= 3.4e+154))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -4.8e+72) || ~((y <= 3.4e+154)))
		tmp = t * (y / a);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4.8e+72], N[Not[LessEqual[y, 3.4e+154]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.8000000000000002e72 or 3.39999999999999974e154 < y

   1. Initial program 76.0%

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

      1. +-commutative 76.0%

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

      2. *-commutative 76.0%

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

      3. associate-/l* 88.4%

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

      4. fma-define 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in t around inf 53.4%

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

   6. Taylor expanded in z around 0 35.3%

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

   if -4.8000000000000002e72 < y < 3.39999999999999974e154

   1. Initial program 65.8%

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

      1. associate-/l* 73.8%

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

   3. Simplified 73.8%

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

   5. Taylor expanded in t around inf 59.3%

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

      1. associate-/l* 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in z around inf 41.3%

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

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+72} \lor \neg \left(y \leq 3.4 \cdot 10^{+154}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 38.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+127}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e+127) t (if (<= z 8.5e-14) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+127) {
		tmp = t;
	} else if (z <= 8.5e-14) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.8d+127)) then
        tmp = t
    else if (z <= 8.5d-14) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+127) {
		tmp = t;
	} else if (z <= 8.5e-14) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.8e+127:
		tmp = t
	elif z <= 8.5e-14:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e+127)
		tmp = t;
	elseif (z <= 8.5e-14)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.8e+127)
		tmp = t;
	elseif (z <= 8.5e-14)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e+127], t, If[LessEqual[z, 8.5e-14], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.79999999999999989e127 or 8.50000000000000038e-14 < z

   1. Initial program 39.4%

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

      1. associate-/l* 65.8%

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

   3. Simplified 65.8%

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

   5. Taylor expanded in t around inf 33.2%

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

      1. associate-/l* 58.6%

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

   7. Simplified 58.6%

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

   8. Taylor expanded in z around inf 43.8%

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

   9. Taylor expanded in x around 0 52.9%

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

   if -1.79999999999999989e127 < z < 8.50000000000000038e-14

   1. Initial program 88.9%

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

      1. +-commutative 88.9%

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

      2. *-commutative 88.9%

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

      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. Taylor expanded in a around inf 29.9%

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

Alternative 21: 24.9% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.8%

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

   1. associate-/l* 79.0%

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

3. Simplified 79.0%

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

5. Taylor expanded in t around inf 54.6%

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

   1. associate-/l* 66.0%

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

7. Simplified 66.0%

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

8. Taylor expanded in z around inf 32.5%

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

9. Taylor expanded in x around 0 26.0%

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

Developer Target 1: 84.1% 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 2024180 
(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))))