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

Percentage Accurate: 68.3% → 90.8%

Time: 17.0s

Alternatives: 23

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-275}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_1 -5e-275)
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (if (<= t_1 0.0)
       (+ t (/ (* (- t x) (- a y)) z))
       (fma (- t x) (/ (- y z) (- 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 <= -5e-275) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = fma((t - x), ((y - z) / (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 <= -5e-275)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	else
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / 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, -5e-275], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.99999999999999983e-275

   1. Initial program 79.6%

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

      1. associate-/l* 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in y around 0 80.2%

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

      1. mul-1-neg 80.2%

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

      2. associate-/l* 85.1%

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

      3. distribute-lft-neg-out 85.1%

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

      4. +-commutative 85.1%

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

      5. div-sub 85.1%

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

      6. distribute-rgt-out 90.2%

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

      7. sub-neg 90.2%

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

      8. associate-/r/ 94.5%

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

   7. Simplified 94.5%

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

   if -4.99999999999999983e-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 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-*r/ 99.5%

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

      3. associate-*r/ 99.5%

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

      4. mul-1-neg 99.5%

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

      5. div-sub 99.5%

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

      6. mul-1-neg 99.5%

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

      7. distribute-lft-out-- 99.5%

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

      8. associate-*r/ 99.5%

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

      9. mul-1-neg 99.5%

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

      10. unsub-neg 99.5%

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

      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)))

   1. Initial program 69.3%

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

      1. +-commutative 69.3%

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

      2. *-commutative 69.3%

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

      3. associate-/l* 90.9%

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

      4. fma-define 91.0%

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

   3. Simplified 91.0%

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

4. Final simplification 93.2%

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

Alternative 2: 91.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+278}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-275}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+304}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z)))))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -5e+278)
     t_1
     (if (<= t_2 -5e-275)
       t_2
       (if (<= t_2 0.0)
         (+ t (/ (* (- t x) (- a y)) z))
         (if (<= t_2 4e+304) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -5e+278) {
		tmp = t_1;
	} else if (t_2 <= -5e-275) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 4e+304) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    t_2 = x + (((y - z) * (t - x)) / (a - z))
    if (t_2 <= (-5d+278)) then
        tmp = t_1
    else if (t_2 <= (-5d-275)) then
        tmp = t_2
    else if (t_2 <= 0.0d0) then
        tmp = t + (((t - x) * (a - y)) / z)
    else if (t_2 <= 4d+304) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -5e+278) {
		tmp = t_1;
	} else if (t_2 <= -5e-275) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 4e+304) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	t_2 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_2 <= -5e+278:
		tmp = t_1
	elif t_2 <= -5e-275:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t + (((t - x) * (a - y)) / z)
	elif t_2 <= 4e+304:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -5e+278)
		tmp = t_1;
	elseif (t_2 <= -5e-275)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (t_2 <= 4e+304)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	t_2 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -5e+278)
		tmp = t_1;
	elseif (t_2 <= -5e-275)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (t_2 <= 4e+304)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+278], t$95$1, If[LessEqual[t$95$2, -5e-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, 4e+304], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -5.00000000000000029e278 or 3.9999999999999998e304 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 48.1%

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

      1. associate-/l* 89.6%

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

   3. Simplified 89.6%

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

   if -5.00000000000000029e278 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.99999999999999983e-275 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 3.9999999999999998e304

   1. Initial program 95.1%

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

   if -4.99999999999999983e-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 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-*r/ 99.5%

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

      3. associate-*r/ 99.5%

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

      4. mul-1-neg 99.5%

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

      5. div-sub 99.5%

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

      6. mul-1-neg 99.5%

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

      7. distribute-lft-out-- 99.5%

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

      8. associate-*r/ 99.5%

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

      9. mul-1-neg 99.5%

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

      10. unsub-neg 99.5%

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

      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 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -5 \cdot 10^{+278}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -5 \cdot 10^{-275}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 4 \cdot 10^{+304}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-275} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -5e-275) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ t (/ (* (- t x) (- a y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -5e-275) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) * (t - x)) / (a - z))
    if ((t_1 <= (-5d-275)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -5e-275) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if (t_1 <= -5e-275) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -5e-275) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -5e-275) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-275], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.99999999999999983e-275 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 74.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 0 75.7%

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

      1. mul-1-neg 75.7%

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

      2. associate-/l* 83.6%

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

      3. distribute-lft-neg-out 83.6%

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

      4. +-commutative 83.6%

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

      5. div-sub 83.6%

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

      6. distribute-rgt-out 87.8%

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

      7. sub-neg 87.8%

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

      8. associate-/r/ 92.7%

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

   7. Simplified 92.7%

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

   if -4.99999999999999983e-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 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-*r/ 99.5%

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

      3. associate-*r/ 99.5%

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

      4. mul-1-neg 99.5%

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

      5. div-sub 99.5%

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

      6. mul-1-neg 99.5%

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

      7. distribute-lft-out-- 99.5%

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

      8. associate-*r/ 99.5%

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

      9. mul-1-neg 99.5%

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

      10. unsub-neg 99.5%

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

      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 2 regimes into one program.

4. Final simplification 93.1%

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

Alternative 4: 57.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+130}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a}{z}\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-88}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -3.05 \cdot 10^{-167}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+143}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.05e+130)
   (+ t (/ (* (- t x) a) z))
   (if (<= z -2.35e-88)
     (+ x (* t (/ y (- a z))))
     (if (<= z -3.05e-167)
       (* x (- 1.0 (/ y a)))
       (if (<= z 3.55e+143)
         (+ x (* t (/ (- y z) a)))
         (+ t (* a (/ (- t x) z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.05e+130) {
		tmp = t + (((t - x) * a) / z);
	} else if (z <= -2.35e-88) {
		tmp = x + (t * (y / (a - z)));
	} else if (z <= -3.05e-167) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 3.55e+143) {
		tmp = x + (t * ((y - z) / a));
	} else {
		tmp = t + (a * ((t - x) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.05d+130)) then
        tmp = t + (((t - x) * a) / z)
    else if (z <= (-2.35d-88)) then
        tmp = x + (t * (y / (a - z)))
    else if (z <= (-3.05d-167)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 3.55d+143) then
        tmp = x + (t * ((y - z) / a))
    else
        tmp = t + (a * ((t - x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.05e+130) {
		tmp = t + (((t - x) * a) / z);
	} else if (z <= -2.35e-88) {
		tmp = x + (t * (y / (a - z)));
	} else if (z <= -3.05e-167) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 3.55e+143) {
		tmp = x + (t * ((y - z) / a));
	} else {
		tmp = t + (a * ((t - x) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.05e+130:
		tmp = t + (((t - x) * a) / z)
	elif z <= -2.35e-88:
		tmp = x + (t * (y / (a - z)))
	elif z <= -3.05e-167:
		tmp = x * (1.0 - (y / a))
	elif z <= 3.55e+143:
		tmp = x + (t * ((y - z) / a))
	else:
		tmp = t + (a * ((t - x) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.05e+130)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * a) / z));
	elseif (z <= -2.35e-88)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	elseif (z <= -3.05e-167)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 3.55e+143)
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / a)));
	else
		tmp = Float64(t + Float64(a * Float64(Float64(t - x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.05e+130)
		tmp = t + (((t - x) * a) / z);
	elseif (z <= -2.35e-88)
		tmp = x + (t * (y / (a - z)));
	elseif (z <= -3.05e-167)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 3.55e+143)
		tmp = x + (t * ((y - z) / a));
	else
		tmp = t + (a * ((t - x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.05e+130], N[(t + N[(N[(N[(t - x), $MachinePrecision] * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.35e-88], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.05e-167], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.55e+143], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(a * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.04999999999999989e130

   1. Initial program 32.9%

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

      1. +-commutative 32.9%

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

      2. *-commutative 32.9%

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

      3. associate-/l* 62.7%

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

      4. fma-define 62.9%

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

   3. Simplified 62.9%

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

   5. Taylor expanded in y around 0 30.1%

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

      1. mul-1-neg 30.1%

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

      2. associate-/l* 36.7%

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

      3. distribute-lft-neg-out 36.7%

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

      4. +-commutative 36.7%

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

      5. *-commutative 36.7%

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

      6. fma-define 36.6%

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

   7. Simplified 36.6%

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

   8. Taylor expanded in z around inf 66.9%

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

   if -2.04999999999999989e130 < z < -2.35e-88

   1. Initial program 71.9%

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

   3. Taylor expanded in y around inf 57.8%

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

      1. *-commutative 57.8%

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

   5. Simplified 57.8%

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

   6. Taylor expanded in t around inf 46.0%

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

      1. associate-/l* 51.9%

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

   8. Simplified 51.9%

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

   if -2.35e-88 < z < -3.0499999999999999e-167

   1. Initial program 75.9%

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

      1. associate-/l* 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in y around 0 83.0%

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

      1. mul-1-neg 83.0%

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

      2. associate-/l* 82.4%

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

      3. distribute-lft-neg-out 82.4%

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

      4. +-commutative 82.4%

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

      5. div-sub 82.4%

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

      6. distribute-rgt-out 82.4%

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

      7. sub-neg 82.4%

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

      8. associate-/r/ 89.5%

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

   7. Simplified 89.5%

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

   8. Taylor expanded in t around inf 85.3%

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

      1. mul-1-neg 85.3%

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

      2. unsub-neg 85.3%

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

   10. Simplified 85.3%

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

   11. Taylor expanded in z around 0 63.5%

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

   12. Taylor expanded in x around inf 73.0%

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

       1. mul-1-neg 73.0%

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

       2. unsub-neg 73.0%

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

   14. Simplified 73.0%

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

   if -3.0499999999999999e-167 < z < 3.55000000000000021e143

   1. Initial program 88.8%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in t around inf 71.2%

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

   6. Taylor expanded in a around inf 60.3%

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

      1. associate-/l* 68.2%

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

   8. Simplified 68.2%

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

   if 3.55000000000000021e143 < z

   1. Initial program 37.1%

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

      1. +-commutative 37.1%

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

      2. *-commutative 37.1%

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

      3. associate-/l* 82.7%

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

      4. fma-define 82.8%

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

   3. Simplified 82.8%

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

   5. Taylor expanded in y around 0 36.4%

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

      1. mul-1-neg 36.4%

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

      2. associate-/l* 63.5%

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

      3. distribute-lft-neg-out 63.5%

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

      4. +-commutative 63.5%

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

      5. *-commutative 63.5%

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

      6. fma-define 63.7%

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

   7. Simplified 63.7%

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

   8. Taylor expanded in z around inf 51.6%

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

      1. associate-/l* 68.2%

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

   10. Simplified 68.2%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+130}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a}{z}\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-88}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -3.05 \cdot 10^{-167}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+143}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+109}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a}{z}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-167}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-33}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+143}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.22e+109)
   (+ t (/ (* (- t x) a) z))
   (if (<= z -1.12e-167)
     (* x (- 1.0 (/ y a)))
     (if (<= z 1.7e-33)
       (+ x (/ t (/ a y)))
       (if (<= z 3.55e+143) (* y (/ (- x t) z)) (+ t (* a (/ (- t x) z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.22e+109) {
		tmp = t + (((t - x) * a) / z);
	} else if (z <= -1.12e-167) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.7e-33) {
		tmp = x + (t / (a / y));
	} else if (z <= 3.55e+143) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t + (a * ((t - x) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.22d+109)) then
        tmp = t + (((t - x) * a) / z)
    else if (z <= (-1.12d-167)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.7d-33) then
        tmp = x + (t / (a / y))
    else if (z <= 3.55d+143) then
        tmp = y * ((x - t) / z)
    else
        tmp = t + (a * ((t - x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.22e+109) {
		tmp = t + (((t - x) * a) / z);
	} else if (z <= -1.12e-167) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.7e-33) {
		tmp = x + (t / (a / y));
	} else if (z <= 3.55e+143) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t + (a * ((t - x) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.22e+109:
		tmp = t + (((t - x) * a) / z)
	elif z <= -1.12e-167:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.7e-33:
		tmp = x + (t / (a / y))
	elif z <= 3.55e+143:
		tmp = y * ((x - t) / z)
	else:
		tmp = t + (a * ((t - x) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.22e+109)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * a) / z));
	elseif (z <= -1.12e-167)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.7e-33)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 3.55e+143)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = Float64(t + Float64(a * Float64(Float64(t - x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.22e+109)
		tmp = t + (((t - x) * a) / z);
	elseif (z <= -1.12e-167)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.7e-33)
		tmp = x + (t / (a / y));
	elseif (z <= 3.55e+143)
		tmp = y * ((x - t) / z);
	else
		tmp = t + (a * ((t - x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.22e+109], N[(t + N[(N[(N[(t - x), $MachinePrecision] * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.12e-167], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e-33], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.55e+143], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t + N[(a * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.2200000000000001e109

   1. Initial program 34.7%

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

      1. +-commutative 34.7%

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

      2. *-commutative 34.7%

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

      3. associate-/l* 63.8%

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

      4. fma-define 63.9%

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

   3. Simplified 63.9%

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

   5. Taylor expanded in y around 0 29.3%

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

      1. mul-1-neg 29.3%

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

      2. associate-/l* 35.8%

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

      3. distribute-lft-neg-out 35.8%

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

      4. +-commutative 35.8%

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

      5. *-commutative 35.8%

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

      6. fma-define 35.6%

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

   7. Simplified 35.6%

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

   8. Taylor expanded in z around inf 65.1%

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

   if -1.2200000000000001e109 < z < -1.1200000000000001e-167

   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* 83.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in y around 0 74.5%

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

      1. mul-1-neg 74.5%

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

      2. associate-/l* 82.9%

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

      3. distribute-lft-neg-out 82.9%

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

      4. +-commutative 82.9%

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

      5. div-sub 82.9%

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

      6. distribute-rgt-out 83.0%

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

      7. sub-neg 83.0%

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

      8. associate-/r/ 88.0%

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

   7. Simplified 88.0%

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

   8. Taylor expanded in t around inf 85.4%

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

      1. mul-1-neg 85.4%

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

      2. unsub-neg 85.4%

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

   10. Simplified 85.4%

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

   11. Taylor expanded in z around 0 50.6%

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

   12. Taylor expanded in x around inf 50.6%

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

       1. mul-1-neg 50.6%

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

       2. unsub-neg 50.6%

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

   14. Simplified 50.6%

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

   if -1.1200000000000001e-167 < z < 1.7e-33

   1. Initial program 90.3%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in y around 0 93.0%

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

      1. mul-1-neg 93.0%

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

      2. associate-/l* 83.9%

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

      3. distribute-lft-neg-out 83.9%

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

      4. +-commutative 83.9%

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

      5. div-sub 83.9%

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

      6. distribute-rgt-out 95.2%

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

      7. sub-neg 95.2%

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

      8. associate-/r/ 96.4%

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

   7. Simplified 96.4%

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

   8. Taylor expanded in t around inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. unsub-neg 90.1%

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

   10. Simplified 90.1%

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

   11. Taylor expanded in z around 0 76.1%

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

   12. Taylor expanded in t around inf 72.1%

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

   if 1.7e-33 < z < 3.55000000000000021e143

   1. Initial program 84.2%

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

      1. +-commutative 84.2%

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

      2. *-commutative 84.2%

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

      3. associate-/l* 90.8%

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

      4. fma-define 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in y around inf 57.3%

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

   6. Taylor expanded in a around 0 43.9%

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

      1. associate-*r/ 43.9%

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

      2. associate-*r/ 43.9%

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

      3. div-sub 43.9%

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

      4. cancel-sign-sub-inv 43.9%

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

      5. neg-mul-1 43.9%

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

      6. metadata-eval 43.9%

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

      7. *-commutative 43.9%

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

      8. *-rgt-identity 43.9%

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

   8. Simplified 43.9%

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

   if 3.55000000000000021e143 < z

   1. Initial program 37.1%

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

      1. +-commutative 37.1%

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

      2. *-commutative 37.1%

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

      3. associate-/l* 82.7%

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

      4. fma-define 82.8%

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

   3. Simplified 82.8%

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

   5. Taylor expanded in y around 0 36.4%

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

      1. mul-1-neg 36.4%

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

      2. associate-/l* 63.5%

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

      3. distribute-lft-neg-out 63.5%

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

      4. +-commutative 63.5%

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

      5. *-commutative 63.5%

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

      6. fma-define 63.7%

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

   7. Simplified 63.7%

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

   8. Taylor expanded in z around inf 51.6%

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

      1. associate-/l* 68.2%

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

   10. Simplified 68.2%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+109}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a}{z}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-167}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-33}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+143}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(\frac{t}{x} - \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-168}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+143}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.45e+70)
   (* x (- (/ t x) (/ a z)))
   (if (<= z -1.5e-168)
     (* x (- 1.0 (/ y a)))
     (if (<= z 3.2e-30)
       (+ x (/ t (/ a y)))
       (if (<= z 3.55e+143) (* y (/ (- x t) z)) (+ t (* a (/ (- t x) z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.45e+70) {
		tmp = x * ((t / x) - (a / z));
	} else if (z <= -1.5e-168) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 3.2e-30) {
		tmp = x + (t / (a / y));
	} else if (z <= 3.55e+143) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t + (a * ((t - x) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.45d+70)) then
        tmp = x * ((t / x) - (a / z))
    else if (z <= (-1.5d-168)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 3.2d-30) then
        tmp = x + (t / (a / y))
    else if (z <= 3.55d+143) then
        tmp = y * ((x - t) / z)
    else
        tmp = t + (a * ((t - x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.45e+70) {
		tmp = x * ((t / x) - (a / z));
	} else if (z <= -1.5e-168) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 3.2e-30) {
		tmp = x + (t / (a / y));
	} else if (z <= 3.55e+143) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t + (a * ((t - x) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.45e+70:
		tmp = x * ((t / x) - (a / z))
	elif z <= -1.5e-168:
		tmp = x * (1.0 - (y / a))
	elif z <= 3.2e-30:
		tmp = x + (t / (a / y))
	elif z <= 3.55e+143:
		tmp = y * ((x - t) / z)
	else:
		tmp = t + (a * ((t - x) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.45e+70)
		tmp = Float64(x * Float64(Float64(t / x) - Float64(a / z)));
	elseif (z <= -1.5e-168)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 3.2e-30)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 3.55e+143)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = Float64(t + Float64(a * Float64(Float64(t - x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.45e+70)
		tmp = x * ((t / x) - (a / z));
	elseif (z <= -1.5e-168)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 3.2e-30)
		tmp = x + (t / (a / y));
	elseif (z <= 3.55e+143)
		tmp = y * ((x - t) / z);
	else
		tmp = t + (a * ((t - x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.45e+70], N[(x * N[(N[(t / x), $MachinePrecision] - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.5e-168], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-30], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.55e+143], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t + N[(a * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.45000000000000014e70

   1. Initial program 38.7%

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

      1. +-commutative 38.7%

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

      2. *-commutative 38.7%

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

      3. associate-/l* 65.4%

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

      4. fma-define 65.5%

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

   3. Simplified 65.5%

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

   5. Taylor expanded in y around 0 30.0%

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

      1. mul-1-neg 30.0%

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

      2. associate-/l* 31.1%

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

      3. distribute-lft-neg-out 31.1%

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

      4. +-commutative 31.1%

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

      5. *-commutative 31.1%

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

      6. fma-define 31.1%

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

   7. Simplified 31.1%

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

   8. Taylor expanded in z around inf 57.9%

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

      1. associate-/l* 57.2%

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

   10. Simplified 57.2%

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

   11. Taylor expanded in t around 0 57.8%

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

       1. mul-1-neg 57.8%

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

       2. associate-/l* 56.9%

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

       3. distribute-rgt-neg-in 56.9%

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

       4. mul-1-neg 56.9%

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

       5. associate-*r/ 56.9%

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

       6. mul-1-neg 56.9%

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

   13. Simplified 56.9%

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

   14. Taylor expanded in x around inf 57.8%

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

       1. +-commutative 57.8%

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

       2. mul-1-neg 57.8%

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

       3. unsub-neg 57.8%

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

   16. Simplified 57.8%

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

   if -2.45000000000000014e70 < z < -1.49999999999999996e-168

   1. Initial program 76.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 0 76.7%

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

      1. mul-1-neg 76.7%

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

      2. associate-/l* 86.6%

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

      3. distribute-lft-neg-out 86.6%

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

      4. +-commutative 86.6%

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

      5. div-sub 86.6%

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

      6. distribute-rgt-out 86.8%

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

      7. sub-neg 86.8%

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

      8. associate-/r/ 90.9%

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

   7. Simplified 90.9%

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

   8. Taylor expanded in t around inf 87.8%

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

      1. mul-1-neg 87.8%

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

      2. unsub-neg 87.8%

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

   10. Simplified 87.8%

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

   11. Taylor expanded in z around 0 52.0%

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

   12. Taylor expanded in x around inf 53.6%

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

       1. mul-1-neg 53.6%

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

       2. unsub-neg 53.6%

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

   14. Simplified 53.6%

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

   if -1.49999999999999996e-168 < z < 3.2e-30

   1. Initial program 90.3%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in y around 0 93.0%

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

      1. mul-1-neg 93.0%

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

      2. associate-/l* 83.9%

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

      3. distribute-lft-neg-out 83.9%

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

      4. +-commutative 83.9%

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

      5. div-sub 83.9%

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

      6. distribute-rgt-out 95.2%

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

      7. sub-neg 95.2%

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

      8. associate-/r/ 96.4%

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

   7. Simplified 96.4%

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

   8. Taylor expanded in t around inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. unsub-neg 90.1%

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

   10. Simplified 90.1%

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

   11. Taylor expanded in z around 0 76.1%

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

   12. Taylor expanded in t around inf 72.1%

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

   if 3.2e-30 < z < 3.55000000000000021e143

   1. Initial program 84.2%

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

      1. +-commutative 84.2%

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

      2. *-commutative 84.2%

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

      3. associate-/l* 90.8%

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

      4. fma-define 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in y around inf 57.3%

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

   6. Taylor expanded in a around 0 43.9%

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

      1. associate-*r/ 43.9%

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

      2. associate-*r/ 43.9%

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

      3. div-sub 43.9%

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

      4. cancel-sign-sub-inv 43.9%

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

      5. neg-mul-1 43.9%

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

      6. metadata-eval 43.9%

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

      7. *-commutative 43.9%

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

      8. *-rgt-identity 43.9%

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

   8. Simplified 43.9%

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

   if 3.55000000000000021e143 < z

   1. Initial program 37.1%

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

      1. +-commutative 37.1%

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

      2. *-commutative 37.1%

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

      3. associate-/l* 82.7%

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

      4. fma-define 82.8%

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

   3. Simplified 82.8%

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

   5. Taylor expanded in y around 0 36.4%

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

      1. mul-1-neg 36.4%

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

      2. associate-/l* 63.5%

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

      3. distribute-lft-neg-out 63.5%

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

      4. +-commutative 63.5%

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

      5. *-commutative 63.5%

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

      6. fma-define 63.7%

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

   7. Simplified 63.7%

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

   8. Taylor expanded in z around inf 51.6%

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

      1. associate-/l* 68.2%

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

   10. Simplified 68.2%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(\frac{t}{x} - \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-168}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+143}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(\frac{t}{x} - \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{-167}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+143}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.4e+70)
   (* x (- (/ t x) (/ a z)))
   (if (<= z -2.95e-167)
     (* x (- 1.0 (/ y a)))
     (if (<= z 8e-30)
       (+ x (/ t (/ a y)))
       (if (<= z 3.55e+143) (* y (/ (- x t) z)) (- t (* a (/ x z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e+70) {
		tmp = x * ((t / x) - (a / z));
	} else if (z <= -2.95e-167) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 8e-30) {
		tmp = x + (t / (a / y));
	} else if (z <= 3.55e+143) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t - (a * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.4d+70)) then
        tmp = x * ((t / x) - (a / z))
    else if (z <= (-2.95d-167)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 8d-30) then
        tmp = x + (t / (a / y))
    else if (z <= 3.55d+143) then
        tmp = y * ((x - t) / z)
    else
        tmp = t - (a * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e+70) {
		tmp = x * ((t / x) - (a / z));
	} else if (z <= -2.95e-167) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 8e-30) {
		tmp = x + (t / (a / y));
	} else if (z <= 3.55e+143) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t - (a * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.4e+70:
		tmp = x * ((t / x) - (a / z))
	elif z <= -2.95e-167:
		tmp = x * (1.0 - (y / a))
	elif z <= 8e-30:
		tmp = x + (t / (a / y))
	elif z <= 3.55e+143:
		tmp = y * ((x - t) / z)
	else:
		tmp = t - (a * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.4e+70)
		tmp = Float64(x * Float64(Float64(t / x) - Float64(a / z)));
	elseif (z <= -2.95e-167)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 8e-30)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 3.55e+143)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = Float64(t - Float64(a * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.4e+70)
		tmp = x * ((t / x) - (a / z));
	elseif (z <= -2.95e-167)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 8e-30)
		tmp = x + (t / (a / y));
	elseif (z <= 3.55e+143)
		tmp = y * ((x - t) / z);
	else
		tmp = t - (a * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.4e+70], N[(x * N[(N[(t / x), $MachinePrecision] - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.95e-167], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-30], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.55e+143], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t - N[(a * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.3999999999999999e70

   1. Initial program 38.7%

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

      1. +-commutative 38.7%

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

      2. *-commutative 38.7%

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

      3. associate-/l* 65.4%

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

      4. fma-define 65.5%

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

   3. Simplified 65.5%

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

   5. Taylor expanded in y around 0 30.0%

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

      1. mul-1-neg 30.0%

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

      2. associate-/l* 31.1%

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

      3. distribute-lft-neg-out 31.1%

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

      4. +-commutative 31.1%

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

      5. *-commutative 31.1%

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

      6. fma-define 31.1%

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

   7. Simplified 31.1%

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

   8. Taylor expanded in z around inf 57.9%

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

      1. associate-/l* 57.2%

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

   10. Simplified 57.2%

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

   11. Taylor expanded in t around 0 57.8%

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

       1. mul-1-neg 57.8%

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

       2. associate-/l* 56.9%

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

       3. distribute-rgt-neg-in 56.9%

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

       4. mul-1-neg 56.9%

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

       5. associate-*r/ 56.9%

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

       6. mul-1-neg 56.9%

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

   13. Simplified 56.9%

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

   14. Taylor expanded in x around inf 57.8%

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

       1. +-commutative 57.8%

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

       2. mul-1-neg 57.8%

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

       3. unsub-neg 57.8%

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

   16. Simplified 57.8%

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

   if -5.3999999999999999e70 < z < -2.95000000000000011e-167

   1. Initial program 76.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 0 76.7%

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

      1. mul-1-neg 76.7%

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

      2. associate-/l* 86.6%

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

      3. distribute-lft-neg-out 86.6%

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

      4. +-commutative 86.6%

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

      5. div-sub 86.6%

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

      6. distribute-rgt-out 86.8%

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

      7. sub-neg 86.8%

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

      8. associate-/r/ 90.9%

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

   7. Simplified 90.9%

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

   8. Taylor expanded in t around inf 87.8%

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

      1. mul-1-neg 87.8%

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

      2. unsub-neg 87.8%

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

   10. Simplified 87.8%

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

   11. Taylor expanded in z around 0 52.0%

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

   12. Taylor expanded in x around inf 53.6%

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

       1. mul-1-neg 53.6%

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

       2. unsub-neg 53.6%

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

   14. Simplified 53.6%

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

   if -2.95000000000000011e-167 < z < 8.000000000000001e-30

   1. Initial program 90.3%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in y around 0 93.0%

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

      1. mul-1-neg 93.0%

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

      2. associate-/l* 83.9%

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

      3. distribute-lft-neg-out 83.9%

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

      4. +-commutative 83.9%

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

      5. div-sub 83.9%

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

      6. distribute-rgt-out 95.2%

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

      7. sub-neg 95.2%

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

      8. associate-/r/ 96.4%

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

   7. Simplified 96.4%

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

   8. Taylor expanded in t around inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. unsub-neg 90.1%

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

   10. Simplified 90.1%

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

   11. Taylor expanded in z around 0 76.1%

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

   12. Taylor expanded in t around inf 72.1%

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

   if 8.000000000000001e-30 < z < 3.55000000000000021e143

   1. Initial program 84.2%

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

      1. +-commutative 84.2%

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

      2. *-commutative 84.2%

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

      3. associate-/l* 90.8%

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

      4. fma-define 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in y around inf 57.3%

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

   6. Taylor expanded in a around 0 43.9%

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

      1. associate-*r/ 43.9%

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

      2. associate-*r/ 43.9%

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

      3. div-sub 43.9%

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

      4. cancel-sign-sub-inv 43.9%

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

      5. neg-mul-1 43.9%

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

      6. metadata-eval 43.9%

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

      7. *-commutative 43.9%

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

      8. *-rgt-identity 43.9%

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

   8. Simplified 43.9%

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

   if 3.55000000000000021e143 < z

   1. Initial program 37.1%

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

      1. +-commutative 37.1%

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

      2. *-commutative 37.1%

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

      3. associate-/l* 82.7%

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

      4. fma-define 82.8%

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

   3. Simplified 82.8%

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

   5. Taylor expanded in y around 0 36.4%

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

      1. mul-1-neg 36.4%

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

      2. associate-/l* 63.5%

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

      3. distribute-lft-neg-out 63.5%

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

      4. +-commutative 63.5%

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

      5. *-commutative 63.5%

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

      6. fma-define 63.7%

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

   7. Simplified 63.7%

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

   8. Taylor expanded in z around inf 51.6%

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

      1. associate-/l* 68.2%

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

   10. Simplified 68.2%

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

   11. Taylor expanded in t around 0 65.1%

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

       1. mul-1-neg 65.1%

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

       2. associate-/l* 68.1%

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

       3. distribute-rgt-neg-in 68.1%

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

       4. mul-1-neg 68.1%

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

       5. associate-*r/ 68.1%

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

       6. mul-1-neg 68.1%

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

   13. Simplified 68.1%

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

   14. Taylor expanded in t around 0 65.1%

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

       1. mul-1-neg 65.1%

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

       2. associate-*r/ 68.1%

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

       3. sub-neg 68.1%

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

   16. Simplified 68.1%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(\frac{t}{x} - \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{-167}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+143}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-168}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-31}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+143}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a (/ x z)))))
   (if (<= z -1.02e+114)
     t_1
     (if (<= z -3.8e-168)
       (* x (- 1.0 (/ y a)))
       (if (<= z 8e-31)
         (+ x (/ t (/ a y)))
         (if (<= z 3.55e+143) (* y (/ (- x t) z)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * (x / z));
	double tmp;
	if (z <= -1.02e+114) {
		tmp = t_1;
	} else if (z <= -3.8e-168) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 8e-31) {
		tmp = x + (t / (a / y));
	} else if (z <= 3.55e+143) {
		tmp = y * ((x - t) / 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 - (a * (x / z))
    if (z <= (-1.02d+114)) then
        tmp = t_1
    else if (z <= (-3.8d-168)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 8d-31) then
        tmp = x + (t / (a / y))
    else if (z <= 3.55d+143) then
        tmp = y * ((x - t) / 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 - (a * (x / z));
	double tmp;
	if (z <= -1.02e+114) {
		tmp = t_1;
	} else if (z <= -3.8e-168) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 8e-31) {
		tmp = x + (t / (a / y));
	} else if (z <= 3.55e+143) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a * (x / z))
	tmp = 0
	if z <= -1.02e+114:
		tmp = t_1
	elif z <= -3.8e-168:
		tmp = x * (1.0 - (y / a))
	elif z <= 8e-31:
		tmp = x + (t / (a / y))
	elif z <= 3.55e+143:
		tmp = y * ((x - t) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a * Float64(x / z)))
	tmp = 0.0
	if (z <= -1.02e+114)
		tmp = t_1;
	elseif (z <= -3.8e-168)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 8e-31)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 3.55e+143)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a * (x / z));
	tmp = 0.0;
	if (z <= -1.02e+114)
		tmp = t_1;
	elseif (z <= -3.8e-168)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 8e-31)
		tmp = x + (t / (a / y));
	elseif (z <= 3.55e+143)
		tmp = y * ((x - t) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.02e+114], t$95$1, If[LessEqual[z, -3.8e-168], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-31], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.55e+143], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.01999999999999999e114 or 3.55000000000000021e143 < z

   1. Initial program 35.9%

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

      1. +-commutative 35.9%

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

      2. *-commutative 35.9%

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

      3. associate-/l* 73.1%

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

      4. fma-define 73.2%

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

   3. Simplified 73.2%

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

   5. Taylor expanded in y around 0 32.8%

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

      1. mul-1-neg 32.8%

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

      2. associate-/l* 49.5%

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

      3. distribute-lft-neg-out 49.5%

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

      4. +-commutative 49.5%

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

      5. *-commutative 49.5%

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

      6. fma-define 49.5%

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

   7. Simplified 49.5%

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

   8. Taylor expanded in z around inf 58.5%

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

      1. associate-/l* 66.2%

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

   10. Simplified 66.2%

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

   11. Taylor expanded in t around 0 64.9%

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

       1. mul-1-neg 64.9%

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

       2. associate-/l* 65.8%

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

       3. distribute-rgt-neg-in 65.8%

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

       4. mul-1-neg 65.8%

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

       5. associate-*r/ 65.8%

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

       6. mul-1-neg 65.8%

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

   13. Simplified 65.8%

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

   14. Taylor expanded in t around 0 64.9%

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

       1. mul-1-neg 64.9%

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

       2. associate-*r/ 65.8%

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

       3. sub-neg 65.8%

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

   16. Simplified 65.8%

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

   if -1.01999999999999999e114 < z < -3.8e-168

   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* 83.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in y around 0 74.5%

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

      1. mul-1-neg 74.5%

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

      2. associate-/l* 82.9%

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

      3. distribute-lft-neg-out 82.9%

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

      4. +-commutative 82.9%

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

      5. div-sub 82.9%

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

      6. distribute-rgt-out 83.0%

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

      7. sub-neg 83.0%

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

      8. associate-/r/ 88.0%

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

   7. Simplified 88.0%

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

   8. Taylor expanded in t around inf 85.4%

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

      1. mul-1-neg 85.4%

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

      2. unsub-neg 85.4%

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

   10. Simplified 85.4%

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

   11. Taylor expanded in z around 0 50.6%

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

   12. Taylor expanded in x around inf 50.6%

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

       1. mul-1-neg 50.6%

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

       2. unsub-neg 50.6%

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

   14. Simplified 50.6%

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

   if -3.8e-168 < z < 8.000000000000001e-31

   1. Initial program 90.3%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in y around 0 93.0%

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

      1. mul-1-neg 93.0%

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

      2. associate-/l* 83.9%

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

      3. distribute-lft-neg-out 83.9%

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

      4. +-commutative 83.9%

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

      5. div-sub 83.9%

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

      6. distribute-rgt-out 95.2%

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

      7. sub-neg 95.2%

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

      8. associate-/r/ 96.4%

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

   7. Simplified 96.4%

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

   8. Taylor expanded in t around inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. unsub-neg 90.1%

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

   10. Simplified 90.1%

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

   11. Taylor expanded in z around 0 76.1%

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

   12. Taylor expanded in t around inf 72.1%

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

   if 8.000000000000001e-31 < z < 3.55000000000000021e143

   1. Initial program 84.2%

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

      1. +-commutative 84.2%

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

      2. *-commutative 84.2%

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

      3. associate-/l* 90.8%

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

      4. fma-define 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in y around inf 57.3%

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

   6. Taylor expanded in a around 0 43.9%

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

      1. associate-*r/ 43.9%

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

      2. associate-*r/ 43.9%

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

      3. div-sub 43.9%

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

      4. cancel-sign-sub-inv 43.9%

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

      5. neg-mul-1 43.9%

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

      6. metadata-eval 43.9%

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

      7. *-commutative 43.9%

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

      8. *-rgt-identity 43.9%

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

   8. Simplified 43.9%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+114}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-168}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-31}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+143}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-167}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+143}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a (/ x z)))))
   (if (<= z -5.5e+108)
     t_1
     (if (<= z -3e-167)
       (* x (- 1.0 (/ y a)))
       (if (<= z 3.55e+143) (+ x (* t (/ y a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * (x / z));
	double tmp;
	if (z <= -5.5e+108) {
		tmp = t_1;
	} else if (z <= -3e-167) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 3.55e+143) {
		tmp = x + (t * (y / a));
	} 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 - (a * (x / z))
    if (z <= (-5.5d+108)) then
        tmp = t_1
    else if (z <= (-3d-167)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 3.55d+143) then
        tmp = x + (t * (y / a))
    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 - (a * (x / z));
	double tmp;
	if (z <= -5.5e+108) {
		tmp = t_1;
	} else if (z <= -3e-167) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 3.55e+143) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a * (x / z))
	tmp = 0
	if z <= -5.5e+108:
		tmp = t_1
	elif z <= -3e-167:
		tmp = x * (1.0 - (y / a))
	elif z <= 3.55e+143:
		tmp = x + (t * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a * Float64(x / z)))
	tmp = 0.0
	if (z <= -5.5e+108)
		tmp = t_1;
	elseif (z <= -3e-167)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 3.55e+143)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a * (x / z));
	tmp = 0.0;
	if (z <= -5.5e+108)
		tmp = t_1;
	elseif (z <= -3e-167)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 3.55e+143)
		tmp = x + (t * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e+108], t$95$1, If[LessEqual[z, -3e-167], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.55e+143], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4999999999999998e108 or 3.55000000000000021e143 < z

   1. Initial program 35.9%

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

      1. +-commutative 35.9%

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

      2. *-commutative 35.9%

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

      3. associate-/l* 73.1%

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

      4. fma-define 73.2%

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

   3. Simplified 73.2%

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

   5. Taylor expanded in y around 0 32.8%

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

      1. mul-1-neg 32.8%

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

      2. associate-/l* 49.5%

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

      3. distribute-lft-neg-out 49.5%

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

      4. +-commutative 49.5%

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

      5. *-commutative 49.5%

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

      6. fma-define 49.5%

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

   7. Simplified 49.5%

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

   8. Taylor expanded in z around inf 58.5%

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

      1. associate-/l* 66.2%

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

   10. Simplified 66.2%

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

   11. Taylor expanded in t around 0 64.9%

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

       1. mul-1-neg 64.9%

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

       2. associate-/l* 65.8%

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

       3. distribute-rgt-neg-in 65.8%

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

       4. mul-1-neg 65.8%

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

       5. associate-*r/ 65.8%

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

       6. mul-1-neg 65.8%

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

   13. Simplified 65.8%

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

   14. Taylor expanded in t around 0 64.9%

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

       1. mul-1-neg 64.9%

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

       2. associate-*r/ 65.8%

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

       3. sub-neg 65.8%

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

   16. Simplified 65.8%

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

   if -5.4999999999999998e108 < z < -2.9999999999999998e-167

   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* 83.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in y around 0 74.5%

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

      1. mul-1-neg 74.5%

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

      2. associate-/l* 82.9%

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

      3. distribute-lft-neg-out 82.9%

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

      4. +-commutative 82.9%

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

      5. div-sub 82.9%

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

      6. distribute-rgt-out 83.0%

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

      7. sub-neg 83.0%

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

      8. associate-/r/ 88.0%

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

   7. Simplified 88.0%

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

   8. Taylor expanded in t around inf 85.4%

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

      1. mul-1-neg 85.4%

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

      2. unsub-neg 85.4%

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

   10. Simplified 85.4%

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

   11. Taylor expanded in z around 0 50.6%

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

   12. Taylor expanded in x around inf 50.6%

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

       1. mul-1-neg 50.6%

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

       2. unsub-neg 50.6%

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

   14. Simplified 50.6%

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

   if -2.9999999999999998e-167 < z < 3.55000000000000021e143

   1. Initial program 88.8%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in t around inf 71.2%

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

   6. Taylor expanded in z around 0 54.7%

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

      1. associate-/l* 61.8%

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

   8. Simplified 61.8%

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

Alternative 10: 52.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + a \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-168}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+143}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* a (/ t z)))))
   (if (<= z -3.7e+99)
     t_1
     (if (<= z -1.55e-168)
       (* x (- 1.0 (/ y a)))
       (if (<= z 3.55e+143) (+ x (* t (/ y a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (a * (t / z));
	double tmp;
	if (z <= -3.7e+99) {
		tmp = t_1;
	} else if (z <= -1.55e-168) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 3.55e+143) {
		tmp = x + (t * (y / a));
	} 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 + (a * (t / z))
    if (z <= (-3.7d+99)) then
        tmp = t_1
    else if (z <= (-1.55d-168)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 3.55d+143) then
        tmp = x + (t * (y / a))
    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 + (a * (t / z));
	double tmp;
	if (z <= -3.7e+99) {
		tmp = t_1;
	} else if (z <= -1.55e-168) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 3.55e+143) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (a * (t / z))
	tmp = 0
	if z <= -3.7e+99:
		tmp = t_1
	elif z <= -1.55e-168:
		tmp = x * (1.0 - (y / a))
	elif z <= 3.55e+143:
		tmp = x + (t * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(a * Float64(t / z)))
	tmp = 0.0
	if (z <= -3.7e+99)
		tmp = t_1;
	elseif (z <= -1.55e-168)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 3.55e+143)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (a * (t / z));
	tmp = 0.0;
	if (z <= -3.7e+99)
		tmp = t_1;
	elseif (z <= -1.55e-168)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 3.55e+143)
		tmp = x + (t * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.7e+99], t$95$1, If[LessEqual[z, -1.55e-168], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.55e+143], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.7000000000000001e99 or 3.55000000000000021e143 < z

   1. Initial program 37.2%

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

      1. +-commutative 37.2%

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

      2. *-commutative 37.2%

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

      3. associate-/l* 72.9%

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

      4. fma-define 73.0%

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

   3. Simplified 73.0%

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

   5. Taylor expanded in y around 0 32.9%

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

      1. mul-1-neg 32.9%

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

      2. associate-/l* 47.6%

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

      3. distribute-lft-neg-out 47.6%

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

      4. +-commutative 47.6%

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

      5. *-commutative 47.6%

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

      6. fma-define 47.7%

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

   7. Simplified 47.7%

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

   8. Taylor expanded in z around inf 57.5%

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

      1. associate-/l* 64.9%

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

   10. Simplified 64.9%

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

   11. Taylor expanded in t around inf 53.4%

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

       1. associate-/l* 61.7%

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

   13. Simplified 61.7%

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

   if -3.7000000000000001e99 < z < -1.55e-168

   1. Initial program 73.0%

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

      1. associate-/l* 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in y around 0 74.8%

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

      1. mul-1-neg 74.8%

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

      2. associate-/l* 85.1%

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

      3. distribute-lft-neg-out 85.1%

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

      4. +-commutative 85.1%

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

      5. div-sub 85.1%

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

      6. distribute-rgt-out 85.2%

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

      7. sub-neg 85.2%

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

      8. associate-/r/ 88.9%

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

   7. Simplified 88.9%

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

   8. Taylor expanded in t around inf 86.2%

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

      1. mul-1-neg 86.2%

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

      2. unsub-neg 86.2%

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

   10. Simplified 86.2%

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

   11. Taylor expanded in z around 0 51.3%

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

   12. Taylor expanded in x around inf 51.2%

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

       1. mul-1-neg 51.2%

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

       2. unsub-neg 51.2%

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

   14. Simplified 51.2%

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

   if -1.55e-168 < z < 3.55000000000000021e143

   1. Initial program 88.8%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in t around inf 71.2%

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

   6. Taylor expanded in z around 0 54.7%

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

      1. associate-/l* 61.8%

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

   8. Simplified 61.8%

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

Alternative 11: 74.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+136} \lor \neg \left(y \leq 1.5 \cdot 10^{+53}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4.8e+136) (not (<= y 1.5e+53)))
   (+ x (/ y (/ (- a z) (- t x))))
   (+ x (/ t (/ (- a z) (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.8e+136) || !(y <= 1.5e+53)) {
		tmp = x + (y / ((a - z) / (t - x)));
	} else {
		tmp = x + (t / ((a - z) / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-4.8d+136)) .or. (.not. (y <= 1.5d+53))) then
        tmp = x + (y / ((a - z) / (t - x)))
    else
        tmp = x + (t / ((a - z) / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.8e+136) || !(y <= 1.5e+53)) {
		tmp = x + (y / ((a - z) / (t - x)));
	} else {
		tmp = x + (t / ((a - z) / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4.8e+136) or not (y <= 1.5e+53):
		tmp = x + (y / ((a - z) / (t - x)))
	else:
		tmp = x + (t / ((a - z) / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4.8e+136) || !(y <= 1.5e+53))
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -4.8e+136) || ~((y <= 1.5e+53)))
		tmp = x + (y / ((a - z) / (t - x)));
	else
		tmp = x + (t / ((a - z) / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4.8e+136], N[Not[LessEqual[y, 1.5e+53]], $MachinePrecision]], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.8000000000000001e136 or 1.49999999999999999e53 < y

   1. Initial program 73.5%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

      1. clear-num 92.2%

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

      2. un-div-inv 92.3%

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

   6. Applied egg-rr 92.3%

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

   7. Taylor expanded in y around inf 87.8%

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

   if -4.8000000000000001e136 < y < 1.49999999999999999e53

   1. Initial program 67.9%

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

      1. associate-/l* 76.5%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in y around 0 66.6%

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

      1. mul-1-neg 66.6%

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

      2. associate-/l* 73.3%

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

      3. distribute-lft-neg-out 73.3%

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

      4. +-commutative 73.3%

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

      5. div-sub 73.3%

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

      6. distribute-rgt-out 76.5%

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

      7. sub-neg 76.5%

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

      8. associate-/r/ 81.9%

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

   7. Simplified 81.9%

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

   8. Taylor expanded in t around inf 72.1%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+136} \lor \neg \left(y \leq 1.5 \cdot 10^{+53}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 72.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.86 \cdot 10^{+143} \lor \neg \left(x \leq 7 \cdot 10^{+70}\right):\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.86e+143) (not (<= x 7e+70)))
   (* x (+ (/ (- y z) (- z a)) 1.0))
   (+ x (/ t (/ (- a z) (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.86e+143) || !(x <= 7e+70)) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else {
		tmp = x + (t / ((a - z) / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-1.86d+143)) .or. (.not. (x <= 7d+70))) then
        tmp = x * (((y - z) / (z - a)) + 1.0d0)
    else
        tmp = x + (t / ((a - z) / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.86e+143) || !(x <= 7e+70)) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else {
		tmp = x + (t / ((a - z) / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.86e+143) or not (x <= 7e+70):
		tmp = x * (((y - z) / (z - a)) + 1.0)
	else:
		tmp = x + (t / ((a - z) / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.86e+143) || !(x <= 7e+70))
		tmp = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0));
	else
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.86e+143) || ~((x <= 7e+70)))
		tmp = x * (((y - z) / (z - a)) + 1.0);
	else
		tmp = x + (t / ((a - z) / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.86e+143], N[Not[LessEqual[x, 7e+70]], $MachinePrecision]], N[(x * N[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8599999999999999e143 or 7.00000000000000005e70 < x

   1. Initial program 63.3%

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

      1. +-commutative 63.3%

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

      2. *-commutative 63.3%

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

      3. associate-/l* 81.9%

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

      4. fma-define 82.0%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in t around 0 58.6%

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

      1. *-rgt-identity 58.6%

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

      2. mul-1-neg 58.6%

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

      3. associate-/l* 71.5%

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

      4. distribute-rgt-neg-in 71.5%

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

      5. mul-1-neg 71.5%

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

      6. distribute-lft-in 71.6%

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

      7. mul-1-neg 71.6%

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

      8. unsub-neg 71.6%

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

   7. Simplified 71.6%

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

   if -1.8599999999999999e143 < x < 7.00000000000000005e70

   1. Initial program 73.6%

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

      1. associate-/l* 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in y around 0 75.7%

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

      1. mul-1-neg 75.7%

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

      2. associate-/l* 82.1%

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

      3. distribute-lft-neg-out 82.1%

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

      4. +-commutative 82.1%

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

      5. div-sub 82.1%

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

      6. distribute-rgt-out 84.5%

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

      7. sub-neg 84.5%

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

      8. associate-/r/ 90.0%

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

   7. Simplified 90.0%

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

   8. Taylor expanded in t around inf 79.4%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.86 \cdot 10^{+143} \lor \neg \left(x \leq 7 \cdot 10^{+70}\right):\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 72.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+143} \lor \neg \left(x \leq 4 \cdot 10^{+70}\right):\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.45e+143) (not (<= x 4e+70)))
   (* x (+ (/ (- y z) (- z a)) 1.0))
   (+ x (* t (/ (- y z) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.45e+143) || !(x <= 4e+70)) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else {
		tmp = x + (t * ((y - z) / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-1.45d+143)) .or. (.not. (x <= 4d+70))) then
        tmp = x * (((y - z) / (z - a)) + 1.0d0)
    else
        tmp = x + (t * ((y - z) / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.45e+143) || !(x <= 4e+70)) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else {
		tmp = x + (t * ((y - z) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.45e+143) or not (x <= 4e+70):
		tmp = x * (((y - z) / (z - a)) + 1.0)
	else:
		tmp = x + (t * ((y - z) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.45e+143) || !(x <= 4e+70))
		tmp = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0));
	else
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.45e+143) || ~((x <= 4e+70)))
		tmp = x * (((y - z) / (z - a)) + 1.0);
	else
		tmp = x + (t * ((y - z) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.45e+143], N[Not[LessEqual[x, 4e+70]], $MachinePrecision]], N[(x * N[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4499999999999999e143 or 4.00000000000000029e70 < x

   1. Initial program 63.3%

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

      1. +-commutative 63.3%

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

      2. *-commutative 63.3%

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

      3. associate-/l* 81.9%

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

      4. fma-define 82.0%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in t around 0 58.6%

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

      1. *-rgt-identity 58.6%

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

      2. mul-1-neg 58.6%

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

      3. associate-/l* 71.5%

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

      4. distribute-rgt-neg-in 71.5%

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

      5. mul-1-neg 71.5%

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

      6. distribute-lft-in 71.6%

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

      7. mul-1-neg 71.6%

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

      8. unsub-neg 71.6%

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

   7. Simplified 71.6%

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

   if -1.4499999999999999e143 < x < 4.00000000000000029e70

   1. Initial program 73.6%

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

      1. associate-/l* 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in t around inf 63.2%

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

      1. associate-/l* 78.9%

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

   7. Simplified 78.9%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+143} \lor \neg \left(x \leq 4 \cdot 10^{+70}\right):\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-87}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-140}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.2e-87)
   (+ x (* t (/ (- y z) (- a z))))
   (if (<= a 1.85e-140)
     (+ t (/ (* (- t x) (- a y)) z))
     (+ x (/ t (/ (- a z) (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e-87) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else if (a <= 1.85e-140) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + (t / ((a - z) / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.2d-87)) then
        tmp = x + (t * ((y - z) / (a - z)))
    else if (a <= 1.85d-140) then
        tmp = t + (((t - x) * (a - y)) / z)
    else
        tmp = x + (t / ((a - z) / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e-87) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else if (a <= 1.85e-140) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + (t / ((a - z) / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.2e-87:
		tmp = x + (t * ((y - z) / (a - z)))
	elif a <= 1.85e-140:
		tmp = t + (((t - x) * (a - y)) / z)
	else:
		tmp = x + (t / ((a - z) / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.2e-87)
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	elseif (a <= 1.85e-140)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	else
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.2e-87)
		tmp = x + (t * ((y - z) / (a - z)));
	elseif (a <= 1.85e-140)
		tmp = t + (((t - x) * (a - y)) / z);
	else
		tmp = x + (t / ((a - z) / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.2e-87], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e-140], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.19999999999999979e-87

   1. Initial program 69.1%

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

      1. associate-/l* 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in t around inf 63.3%

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

      1. associate-/l* 75.3%

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

   7. Simplified 75.3%

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

   if -3.19999999999999979e-87 < a < 1.84999999999999989e-140

   1. Initial program 64.8%

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

      1. +-commutative 64.8%

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

      2. *-commutative 64.8%

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

      3. associate-/l* 74.1%

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

      4. fma-define 74.2%

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

   3. Simplified 74.2%

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

   5. Taylor expanded in z around inf 84.6%

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

      1. associate--l+ 84.6%

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

      2. associate-*r/ 84.6%

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

      3. associate-*r/ 84.6%

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

      4. mul-1-neg 84.6%

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

      5. div-sub 84.7%

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

      6. mul-1-neg 84.7%

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

      7. distribute-lft-out-- 84.7%

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

      8. associate-*r/ 84.7%

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

      9. mul-1-neg 84.7%

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

      10. unsub-neg 84.7%

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

      11. distribute-rgt-out-- 84.7%

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

   7. Simplified 84.7%

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

   if 1.84999999999999989e-140 < a

   1. Initial program 75.2%

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

      1. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in y around 0 80.2%

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

      1. mul-1-neg 80.2%

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

      2. associate-/l* 91.2%

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

      3. distribute-lft-neg-out 91.2%

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

      4. +-commutative 91.2%

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

      5. div-sub 91.2%

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

      6. distribute-rgt-out 91.2%

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

      7. sub-neg 91.2%

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

      8. associate-/r/ 95.2%

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

   7. Simplified 95.2%

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

   8. Taylor expanded in t around inf 82.5%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-87}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-140}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 74.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+132}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+53}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.7e+132)
   (+ x (/ (- t x) (/ (- a z) y)))
   (if (<= y 5.5e+53)
     (+ x (/ t (/ (- a z) (- y z))))
     (+ x (/ y (/ (- a z) (- t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.7e+132) {
		tmp = x + ((t - x) / ((a - z) / y));
	} else if (y <= 5.5e+53) {
		tmp = x + (t / ((a - z) / (y - z)));
	} else {
		tmp = x + (y / ((a - z) / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-2.7d+132)) then
        tmp = x + ((t - x) / ((a - z) / y))
    else if (y <= 5.5d+53) then
        tmp = x + (t / ((a - z) / (y - z)))
    else
        tmp = x + (y / ((a - z) / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.7e+132) {
		tmp = x + ((t - x) / ((a - z) / y));
	} else if (y <= 5.5e+53) {
		tmp = x + (t / ((a - z) / (y - z)));
	} else {
		tmp = x + (y / ((a - z) / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.7e+132:
		tmp = x + ((t - x) / ((a - z) / y))
	elif y <= 5.5e+53:
		tmp = x + (t / ((a - z) / (y - z)))
	else:
		tmp = x + (y / ((a - z) / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.7e+132)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / y)));
	elseif (y <= 5.5e+53)
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.7e+132)
		tmp = x + ((t - x) / ((a - z) / y));
	elseif (y <= 5.5e+53)
		tmp = x + (t / ((a - z) / (y - z)));
	else
		tmp = x + (y / ((a - z) / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.7e+132], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+53], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7e132

   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* 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in y around 0 69.1%

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

      1. mul-1-neg 69.1%

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

      2. associate-/l* 82.8%

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

      3. distribute-lft-neg-out 82.8%

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

      4. +-commutative 82.8%

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

      5. div-sub 82.8%

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

      6. distribute-rgt-out 88.2%

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

      7. sub-neg 88.2%

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

      8. associate-/r/ 96.8%

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

   7. Simplified 96.8%

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

   8. Taylor expanded in y around inf 89.8%

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

   if -2.7e132 < y < 5.49999999999999975e53

   1. Initial program 67.9%

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

      1. associate-/l* 76.5%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in y around 0 66.6%

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

      1. mul-1-neg 66.6%

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

      2. associate-/l* 73.3%

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

      3. distribute-lft-neg-out 73.3%

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

      4. +-commutative 73.3%

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

      5. div-sub 73.3%

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

      6. distribute-rgt-out 76.5%

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

      7. sub-neg 76.5%

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

      8. associate-/r/ 81.9%

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

   7. Simplified 81.9%

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

   8. Taylor expanded in t around inf 72.1%

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

   if 5.49999999999999975e53 < y

   1. Initial program 76.3%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

      1. clear-num 96.0%

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

      2. un-div-inv 96.0%

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

   6. Applied egg-rr 96.0%

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

   7. Taylor expanded in y around inf 91.5%

      \[\leadsto x + \frac{\color{blue}{y}}{\frac{a - z}{t - x}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 62.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+117}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a}{z}\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+143}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.1e+117)
   (+ t (/ (* (- t x) a) z))
   (if (<= z 3.55e+143) (+ x (/ (- t x) (/ a y))) (+ t (* a (/ (- t x) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+117) {
		tmp = t + (((t - x) * a) / z);
	} else if (z <= 3.55e+143) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t + (a * ((t - x) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.1d+117)) then
        tmp = t + (((t - x) * a) / z)
    else if (z <= 3.55d+143) then
        tmp = x + ((t - x) / (a / y))
    else
        tmp = t + (a * ((t - x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+117) {
		tmp = t + (((t - x) * a) / z);
	} else if (z <= 3.55e+143) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t + (a * ((t - x) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.1e+117:
		tmp = t + (((t - x) * a) / z)
	elif z <= 3.55e+143:
		tmp = x + ((t - x) / (a / y))
	else:
		tmp = t + (a * ((t - x) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.1e+117)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * a) / z));
	elseif (z <= 3.55e+143)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	else
		tmp = Float64(t + Float64(a * Float64(Float64(t - x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.1e+117)
		tmp = t + (((t - x) * a) / z);
	elseif (z <= 3.55e+143)
		tmp = x + ((t - x) / (a / y));
	else
		tmp = t + (a * ((t - x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.1e+117], N[(t + N[(N[(N[(t - x), $MachinePrecision] * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.55e+143], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(a * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.10000000000000007e117

   1. Initial program 34.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 34.7%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. *-commutative 34.7%

         \[\leadsto \frac{\color{blue}{\left(t - x\right) \cdot \left(y - z\right)}}{a - z} + x \]

      3. associate-/l* 63.8%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} + x \]

      4. fma-define 63.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]

   3. Simplified 63.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 29.3%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 29.3%

         \[\leadsto x + \color{blue}{\left(-\frac{z \cdot \left(t - x\right)}{a - z}\right)} \]

      2. associate-/l* 35.8%

         \[\leadsto x + \left(-\color{blue}{z \cdot \frac{t - x}{a - z}}\right) \]

      3. distribute-lft-neg-out 35.8%

         \[\leadsto x + \color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z}} \]

      4. +-commutative 35.8%

         \[\leadsto \color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z} + x} \]

      5. *-commutative 35.8%

         \[\leadsto \color{blue}{\frac{t - x}{a - z} \cdot \left(-z\right)} + x \]

      6. fma-define 35.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, -z, x\right)} \]

   7. Simplified 35.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, -z, x\right)} \]

   8. Taylor expanded in z around inf 65.1%

      \[\leadsto \color{blue}{t + \frac{a \cdot \left(t - x\right)}{z}} \]

   if -1.10000000000000007e117 < z < 3.55000000000000021e143

   1. Initial program 83.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 89.6%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 89.6%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 84.3%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{z \cdot \left(t - x\right)}{a - z} + y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 84.3%

         \[\leadsto x + \left(\color{blue}{\left(-\frac{z \cdot \left(t - x\right)}{a - z}\right)} + y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)\right) \]

      2. associate-/l* 84.1%

         \[\leadsto x + \left(\left(-\color{blue}{z \cdot \frac{t - x}{a - z}}\right) + y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)\right) \]

      3. distribute-lft-neg-out 84.1%

         \[\leadsto x + \left(\color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z}} + y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)\right) \]

      4. +-commutative 84.1%

         \[\leadsto x + \color{blue}{\left(y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) + \left(-z\right) \cdot \frac{t - x}{a - z}\right)} \]

      5. div-sub 84.1%

         \[\leadsto x + \left(y \cdot \color{blue}{\frac{t - x}{a - z}} + \left(-z\right) \cdot \frac{t - x}{a - z}\right) \]

      6. distribute-rgt-out 89.6%

         \[\leadsto x + \color{blue}{\frac{t - x}{a - z} \cdot \left(y + \left(-z\right)\right)} \]

      7. sub-neg 89.6%

         \[\leadsto x + \frac{t - x}{a - z} \cdot \color{blue}{\left(y - z\right)} \]

      8. associate-/r/ 92.5%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   7. Simplified 92.5%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   8. Taylor expanded in z around 0 65.0%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a}{y}}} \]

   if 3.55000000000000021e143 < z

   1. Initial program 37.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 37.1%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. *-commutative 37.1%

         \[\leadsto \frac{\color{blue}{\left(t - x\right) \cdot \left(y - z\right)}}{a - z} + x \]

      3. associate-/l* 82.7%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} + x \]

      4. fma-define 82.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]

   3. Simplified 82.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 36.4%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 36.4%

         \[\leadsto x + \color{blue}{\left(-\frac{z \cdot \left(t - x\right)}{a - z}\right)} \]

      2. associate-/l* 63.5%

         \[\leadsto x + \left(-\color{blue}{z \cdot \frac{t - x}{a - z}}\right) \]

      3. distribute-lft-neg-out 63.5%

         \[\leadsto x + \color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z}} \]

      4. +-commutative 63.5%

         \[\leadsto \color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z} + x} \]

      5. *-commutative 63.5%

         \[\leadsto \color{blue}{\frac{t - x}{a - z} \cdot \left(-z\right)} + x \]

      6. fma-define 63.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, -z, x\right)} \]

   7. Simplified 63.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, -z, x\right)} \]

   8. Taylor expanded in z around inf 51.6%

      \[\leadsto \color{blue}{t + \frac{a \cdot \left(t - x\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 68.2%

         \[\leadsto t + \color{blue}{a \cdot \frac{t - x}{z}} \]

   10. Simplified 68.2%

       \[\leadsto \color{blue}{t + a \cdot \frac{t - x}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+117}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a}{z}\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+143}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 61.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+112}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a}{z}\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+143}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1e+112)
   (+ t (/ (* (- t x) a) z))
   (if (<= z 3.55e+143) (+ x (* y (/ (- t x) a))) (+ t (* a (/ (- t x) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e+112) {
		tmp = t + (((t - x) * a) / z);
	} else if (z <= 3.55e+143) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t + (a * ((t - x) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1d+112)) then
        tmp = t + (((t - x) * a) / z)
    else if (z <= 3.55d+143) then
        tmp = x + (y * ((t - x) / a))
    else
        tmp = t + (a * ((t - x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e+112) {
		tmp = t + (((t - x) * a) / z);
	} else if (z <= 3.55e+143) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t + (a * ((t - x) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1e+112:
		tmp = t + (((t - x) * a) / z)
	elif z <= 3.55e+143:
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = t + (a * ((t - x) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1e+112)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * a) / z));
	elseif (z <= 3.55e+143)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	else
		tmp = Float64(t + Float64(a * Float64(Float64(t - x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1e+112)
		tmp = t + (((t - x) * a) / z);
	elseif (z <= 3.55e+143)
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t + (a * ((t - x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1e+112], N[(t + N[(N[(N[(t - x), $MachinePrecision] * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.55e+143], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(a * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.9999999999999993e111

   1. Initial program 34.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 34.7%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. *-commutative 34.7%

         \[\leadsto \frac{\color{blue}{\left(t - x\right) \cdot \left(y - z\right)}}{a - z} + x \]

      3. associate-/l* 63.8%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} + x \]

      4. fma-define 63.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]

   3. Simplified 63.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 29.3%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 29.3%

         \[\leadsto x + \color{blue}{\left(-\frac{z \cdot \left(t - x\right)}{a - z}\right)} \]

      2. associate-/l* 35.8%

         \[\leadsto x + \left(-\color{blue}{z \cdot \frac{t - x}{a - z}}\right) \]

      3. distribute-lft-neg-out 35.8%

         \[\leadsto x + \color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z}} \]

      4. +-commutative 35.8%

         \[\leadsto \color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z} + x} \]

      5. *-commutative 35.8%

         \[\leadsto \color{blue}{\frac{t - x}{a - z} \cdot \left(-z\right)} + x \]

      6. fma-define 35.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, -z, x\right)} \]

   7. Simplified 35.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, -z, x\right)} \]

   8. Taylor expanded in z around inf 65.1%

      \[\leadsto \color{blue}{t + \frac{a \cdot \left(t - x\right)}{z}} \]

   if -9.9999999999999993e111 < z < 3.55000000000000021e143

   1. Initial program 83.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 89.6%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 89.6%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 57.9%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(t - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 64.4%

         \[\leadsto x + \color{blue}{y \cdot \frac{t - x}{a}} \]

   7. Simplified 64.4%

      \[\leadsto x + \color{blue}{y \cdot \frac{t - x}{a}} \]

   if 3.55000000000000021e143 < z

   1. Initial program 37.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 37.1%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. *-commutative 37.1%

         \[\leadsto \frac{\color{blue}{\left(t - x\right) \cdot \left(y - z\right)}}{a - z} + x \]

      3. associate-/l* 82.7%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} + x \]

      4. fma-define 82.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]

   3. Simplified 82.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 36.4%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 36.4%

         \[\leadsto x + \color{blue}{\left(-\frac{z \cdot \left(t - x\right)}{a - z}\right)} \]

      2. associate-/l* 63.5%

         \[\leadsto x + \left(-\color{blue}{z \cdot \frac{t - x}{a - z}}\right) \]

      3. distribute-lft-neg-out 63.5%

         \[\leadsto x + \color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z}} \]

      4. +-commutative 63.5%

         \[\leadsto \color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z} + x} \]

      5. *-commutative 63.5%

         \[\leadsto \color{blue}{\frac{t - x}{a - z} \cdot \left(-z\right)} + x \]

      6. fma-define 63.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, -z, x\right)} \]

   7. Simplified 63.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, -z, x\right)} \]

   8. Taylor expanded in z around inf 51.6%

      \[\leadsto \color{blue}{t + \frac{a \cdot \left(t - x\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 68.2%

         \[\leadsto t + \color{blue}{a \cdot \frac{t - x}{z}} \]

   10. Simplified 68.2%

       \[\leadsto \color{blue}{t + a \cdot \frac{t - x}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+112}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a}{z}\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+143}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 59.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+130}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a}{z}\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+143}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.5e+130)
   (+ t (/ (* (- t x) a) z))
   (if (<= z 3.55e+143) (+ x (* t (/ y (- a z)))) (+ t (* a (/ (- t x) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+130) {
		tmp = t + (((t - x) * a) / z);
	} else if (z <= 3.55e+143) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = t + (a * ((t - x) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.5d+130)) then
        tmp = t + (((t - x) * a) / z)
    else if (z <= 3.55d+143) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = t + (a * ((t - x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+130) {
		tmp = t + (((t - x) * a) / z);
	} else if (z <= 3.55e+143) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = t + (a * ((t - x) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.5e+130:
		tmp = t + (((t - x) * a) / z)
	elif z <= 3.55e+143:
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = t + (a * ((t - x) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.5e+130)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * a) / z));
	elseif (z <= 3.55e+143)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(t + Float64(a * Float64(Float64(t - x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.5e+130)
		tmp = t + (((t - x) * a) / z);
	elseif (z <= 3.55e+143)
		tmp = x + (t * (y / (a - z)));
	else
		tmp = t + (a * ((t - x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.5e+130], N[(t + N[(N[(N[(t - x), $MachinePrecision] * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.55e+143], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(a * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.50000000000000039e130

   1. Initial program 32.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 32.9%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. *-commutative 32.9%

         \[\leadsto \frac{\color{blue}{\left(t - x\right) \cdot \left(y - z\right)}}{a - z} + x \]

      3. associate-/l* 62.7%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} + x \]

      4. fma-define 62.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]

   3. Simplified 62.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 30.1%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 30.1%

         \[\leadsto x + \color{blue}{\left(-\frac{z \cdot \left(t - x\right)}{a - z}\right)} \]

      2. associate-/l* 36.7%

         \[\leadsto x + \left(-\color{blue}{z \cdot \frac{t - x}{a - z}}\right) \]

      3. distribute-lft-neg-out 36.7%

         \[\leadsto x + \color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z}} \]

      4. +-commutative 36.7%

         \[\leadsto \color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z} + x} \]

      5. *-commutative 36.7%

         \[\leadsto \color{blue}{\frac{t - x}{a - z} \cdot \left(-z\right)} + x \]

      6. fma-define 36.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, -z, x\right)} \]

   7. Simplified 36.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, -z, x\right)} \]

   8. Taylor expanded in z around inf 66.9%

      \[\leadsto \color{blue}{t + \frac{a \cdot \left(t - x\right)}{z}} \]

   if -4.50000000000000039e130 < z < 3.55000000000000021e143

   1. Initial program 83.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 72.0%

      \[\leadsto x + \frac{\color{blue}{y \cdot \left(t - x\right)}}{a - z} \]
   4. Step-by-step derivation

      1. *-commutative 72.0%

         \[\leadsto x + \frac{\color{blue}{\left(t - x\right) \cdot y}}{a - z} \]

   5. Simplified 72.0%

      \[\leadsto x + \frac{\color{blue}{\left(t - x\right) \cdot y}}{a - z} \]

   6. Taylor expanded in t around inf 52.0%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a - z}} \]
   7. Step-by-step derivation

      1. associate-/l* 57.6%

         \[\leadsto x + \color{blue}{t \cdot \frac{y}{a - z}} \]

   8. Simplified 57.6%

      \[\leadsto x + \color{blue}{t \cdot \frac{y}{a - z}} \]

   if 3.55000000000000021e143 < z

   1. Initial program 37.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 37.1%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. *-commutative 37.1%

         \[\leadsto \frac{\color{blue}{\left(t - x\right) \cdot \left(y - z\right)}}{a - z} + x \]

      3. associate-/l* 82.7%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} + x \]

      4. fma-define 82.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]

   3. Simplified 82.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 36.4%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 36.4%

         \[\leadsto x + \color{blue}{\left(-\frac{z \cdot \left(t - x\right)}{a - z}\right)} \]

      2. associate-/l* 63.5%

         \[\leadsto x + \left(-\color{blue}{z \cdot \frac{t - x}{a - z}}\right) \]

      3. distribute-lft-neg-out 63.5%

         \[\leadsto x + \color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z}} \]

      4. +-commutative 63.5%

         \[\leadsto \color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z} + x} \]

      5. *-commutative 63.5%

         \[\leadsto \color{blue}{\frac{t - x}{a - z} \cdot \left(-z\right)} + x \]

      6. fma-define 63.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, -z, x\right)} \]

   7. Simplified 63.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, -z, x\right)} \]

   8. Taylor expanded in z around inf 51.6%

      \[\leadsto \color{blue}{t + \frac{a \cdot \left(t - x\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 68.2%

         \[\leadsto t + \color{blue}{a \cdot \frac{t - x}{z}} \]

   10. Simplified 68.2%

       \[\leadsto \color{blue}{t + a \cdot \frac{t - x}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+130}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a}{z}\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+143}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 81.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+195}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e+195)
   (+ t (/ (* (- t x) (- a y)) z))
   (+ x (* (- y z) (/ (- t x) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+195) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + ((y - z) * ((t - x) / (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 <= (-2.4d+195)) then
        tmp = t + (((t - x) * (a - y)) / z)
    else
        tmp = x + ((y - z) * ((t - x) / (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 <= -2.4e+195) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e+195:
		tmp = t + (((t - x) * (a - y)) / z)
	else:
		tmp = x + ((y - z) * ((t - x) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e+195)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.4e+195)
		tmp = t + (((t - x) * (a - y)) / z);
	else
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e+195], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4000000000000003e195

   1. Initial program 24.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 24.7%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. *-commutative 24.7%

         \[\leadsto \frac{\color{blue}{\left(t - x\right) \cdot \left(y - z\right)}}{a - z} + x \]

      3. associate-/l* 51.7%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} + x \]

      4. fma-define 51.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]

   3. Simplified 51.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 78.8%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 78.8%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 78.8%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 78.8%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. mul-1-neg 78.8%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \frac{\color{blue}{-a \cdot \left(t - x\right)}}{z}\right) \]

      5. div-sub 78.9%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \left(-a \cdot \left(t - x\right)\right)}{z}} \]

      6. mul-1-neg 78.9%

         \[\leadsto t + \frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-lft-out-- 78.9%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      8. associate-*r/ 78.9%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      9. mul-1-neg 78.9%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      10. unsub-neg 78.9%

          \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      11. distribute-rgt-out-- 78.9%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

   7. Simplified 78.9%

      \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

   if -2.4000000000000003e195 < z

   1. Initial program 74.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 87.1%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 87.1%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+195}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 49.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+95} \lor \neg \left(z \leq 2 \cdot 10^{+143}\right):\\ \;\;\;\;t + a \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4e+95) (not (<= z 2e+143)))
   (+ t (* a (/ t z)))
   (* x (- 1.0 (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4e+95) || !(z <= 2e+143)) {
		tmp = t + (a * (t / z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4d+95)) .or. (.not. (z <= 2d+143))) then
        tmp = t + (a * (t / z))
    else
        tmp = x * (1.0d0 - (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4e+95) || !(z <= 2e+143)) {
		tmp = t + (a * (t / z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4e+95) or not (z <= 2e+143):
		tmp = t + (a * (t / z))
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4e+95) || !(z <= 2e+143))
		tmp = Float64(t + Float64(a * Float64(t / z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4e+95) || ~((z <= 2e+143)))
		tmp = t + (a * (t / z));
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4e+95], N[Not[LessEqual[z, 2e+143]], $MachinePrecision]], N[(t + N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.00000000000000008e95 or 2e143 < z

   1. Initial program 38.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 38.0%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. *-commutative 38.0%

         \[\leadsto \frac{\color{blue}{\left(t - x\right) \cdot \left(y - z\right)}}{a - z} + x \]

      3. associate-/l* 73.3%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} + x \]

      4. fma-define 73.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]

   3. Simplified 73.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 32.4%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 32.4%

         \[\leadsto x + \color{blue}{\left(-\frac{z \cdot \left(t - x\right)}{a - z}\right)} \]

      2. associate-/l* 47.0%

         \[\leadsto x + \left(-\color{blue}{z \cdot \frac{t - x}{a - z}}\right) \]

      3. distribute-lft-neg-out 47.0%

         \[\leadsto x + \color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z}} \]

      4. +-commutative 47.0%

         \[\leadsto \color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z} + x} \]

      5. *-commutative 47.0%

         \[\leadsto \color{blue}{\frac{t - x}{a - z} \cdot \left(-z\right)} + x \]

      6. fma-define 47.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, -z, x\right)} \]

   7. Simplified 47.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, -z, x\right)} \]

   8. Taylor expanded in z around inf 56.8%

      \[\leadsto \color{blue}{t + \frac{a \cdot \left(t - x\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 64.1%

         \[\leadsto t + \color{blue}{a \cdot \frac{t - x}{z}} \]

   10. Simplified 64.1%

       \[\leadsto \color{blue}{t + a \cdot \frac{t - x}{z}} \]

   11. Taylor expanded in t around inf 52.7%

       \[\leadsto t + \color{blue}{\frac{a \cdot t}{z}} \]
   12. Step-by-step derivation

       1. associate-/l* 60.8%

          \[\leadsto t + \color{blue}{a \cdot \frac{t}{z}} \]

   13. Simplified 60.8%

       \[\leadsto t + \color{blue}{a \cdot \frac{t}{z}} \]

   if -4.00000000000000008e95 < z < 2e143

   1. Initial program 83.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 90.4%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 90.4%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 85.1%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{z \cdot \left(t - x\right)}{a - z} + y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 85.1%

         \[\leadsto x + \left(\color{blue}{\left(-\frac{z \cdot \left(t - x\right)}{a - z}\right)} + y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)\right) \]

      2. associate-/l* 84.8%

         \[\leadsto x + \left(\left(-\color{blue}{z \cdot \frac{t - x}{a - z}}\right) + y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)\right) \]

      3. distribute-lft-neg-out 84.8%

         \[\leadsto x + \left(\color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z}} + y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)\right) \]

      4. +-commutative 84.8%

         \[\leadsto x + \color{blue}{\left(y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) + \left(-z\right) \cdot \frac{t - x}{a - z}\right)} \]

      5. div-sub 84.8%

         \[\leadsto x + \left(y \cdot \color{blue}{\frac{t - x}{a - z}} + \left(-z\right) \cdot \frac{t - x}{a - z}\right) \]

      6. distribute-rgt-out 90.4%

         \[\leadsto x + \color{blue}{\frac{t - x}{a - z} \cdot \left(y + \left(-z\right)\right)} \]

      7. sub-neg 90.4%

         \[\leadsto x + \frac{t - x}{a - z} \cdot \color{blue}{\left(y - z\right)} \]

      8. associate-/r/ 92.8%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   7. Simplified 92.8%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   8. Taylor expanded in t around inf 88.8%

      \[\leadsto x + \frac{\color{blue}{t \cdot \left(1 + -1 \cdot \frac{x}{t}\right)}}{\frac{a - z}{y - z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 88.8%

         \[\leadsto x + \frac{t \cdot \left(1 + \color{blue}{\left(-\frac{x}{t}\right)}\right)}{\frac{a - z}{y - z}} \]

      2. unsub-neg 88.8%

         \[\leadsto x + \frac{t \cdot \color{blue}{\left(1 - \frac{x}{t}\right)}}{\frac{a - z}{y - z}} \]

   10. Simplified 88.8%

       \[\leadsto x + \frac{\color{blue}{t \cdot \left(1 - \frac{x}{t}\right)}}{\frac{a - z}{y - z}} \]

   11. Taylor expanded in z around 0 61.1%

       \[\leadsto x + \frac{t \cdot \left(1 - \frac{x}{t}\right)}{\color{blue}{\frac{a}{y}}} \]

   12. Taylor expanded in x around inf 53.0%

       \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{a}\right)} \]
   13. Step-by-step derivation

       1. mul-1-neg 53.0%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{y}{a}\right)}\right) \]

       2. unsub-neg 53.0%

          \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y}{a}\right)} \]

   14. Simplified 53.0%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+95} \lor \neg \left(z \leq 2 \cdot 10^{+143}\right):\\ \;\;\;\;t + a \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 49.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+117}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+143}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e+117) t (if (<= z 2.4e+143) (* x (- 1.0 (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+117) {
		tmp = t;
	} else if (z <= 2.4e+143) {
		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 <= (-5.5d+117)) then
        tmp = t
    else if (z <= 2.4d+143) 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 <= -5.5e+117) {
		tmp = t;
	} else if (z <= 2.4e+143) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e+117:
		tmp = t
	elif z <= 2.4e+143:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e+117)
		tmp = t;
	elseif (z <= 2.4e+143)
		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 <= -5.5e+117)
		tmp = t;
	elseif (z <= 2.4e+143)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e+117], t, If[LessEqual[z, 2.4e+143], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -5.49999999999999965e117 or 2.3999999999999998e143 < z

   1. Initial program 36.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 36.8%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. *-commutative 36.8%

         \[\leadsto \frac{\color{blue}{\left(t - x\right) \cdot \left(y - z\right)}}{a - z} + x \]

      3. associate-/l* 73.5%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} + x \]

      4. fma-define 73.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]

   3. Simplified 73.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 32.4%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 32.4%

         \[\leadsto x + \color{blue}{\left(-\frac{z \cdot \left(t - x\right)}{a - z}\right)} \]

      2. associate-/l* 48.8%

         \[\leadsto x + \left(-\color{blue}{z \cdot \frac{t - x}{a - z}}\right) \]

      3. distribute-lft-neg-out 48.8%

         \[\leadsto x + \color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z}} \]

      4. +-commutative 48.8%

         \[\leadsto \color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z} + x} \]

      5. *-commutative 48.8%

         \[\leadsto \color{blue}{\frac{t - x}{a - z} \cdot \left(-z\right)} + x \]

      6. fma-define 48.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, -z, x\right)} \]

   7. Simplified 48.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, -z, x\right)} \]

   8. Taylor expanded in a around 0 61.3%

      \[\leadsto \color{blue}{t} \]

   if -5.49999999999999965e117 < z < 2.3999999999999998e143

   1. Initial program 82.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 89.5%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 89.5%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 84.8%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{z \cdot \left(t - x\right)}{a - z} + y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 84.8%

         \[\leadsto x + \left(\color{blue}{\left(-\frac{z \cdot \left(t - x\right)}{a - z}\right)} + y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)\right) \]

      2. associate-/l* 84.0%

         \[\leadsto x + \left(\left(-\color{blue}{z \cdot \frac{t - x}{a - z}}\right) + y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)\right) \]

      3. distribute-lft-neg-out 84.0%

         \[\leadsto x + \left(\color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z}} + y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)\right) \]

      4. +-commutative 84.0%

         \[\leadsto x + \color{blue}{\left(y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) + \left(-z\right) \cdot \frac{t - x}{a - z}\right)} \]

      5. div-sub 84.0%

         \[\leadsto x + \left(y \cdot \color{blue}{\frac{t - x}{a - z}} + \left(-z\right) \cdot \frac{t - x}{a - z}\right) \]

      6. distribute-rgt-out 89.5%

         \[\leadsto x + \color{blue}{\frac{t - x}{a - z} \cdot \left(y + \left(-z\right)\right)} \]

      7. sub-neg 89.5%

         \[\leadsto x + \frac{t - x}{a - z} \cdot \color{blue}{\left(y - z\right)} \]

      8. associate-/r/ 92.4%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   7. Simplified 92.4%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   8. Taylor expanded in t around inf 88.4%

      \[\leadsto x + \frac{\color{blue}{t \cdot \left(1 + -1 \cdot \frac{x}{t}\right)}}{\frac{a - z}{y - z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 88.4%

         \[\leadsto x + \frac{t \cdot \left(1 + \color{blue}{\left(-\frac{x}{t}\right)}\right)}{\frac{a - z}{y - z}} \]

      2. unsub-neg 88.4%

         \[\leadsto x + \frac{t \cdot \color{blue}{\left(1 - \frac{x}{t}\right)}}{\frac{a - z}{y - z}} \]

   10. Simplified 88.4%

       \[\leadsto x + \frac{\color{blue}{t \cdot \left(1 - \frac{x}{t}\right)}}{\frac{a - z}{y - z}} \]

   11. Taylor expanded in z around 0 60.7%

       \[\leadsto x + \frac{t \cdot \left(1 - \frac{x}{t}\right)}{\color{blue}{\frac{a}{y}}} \]

   12. Taylor expanded in x around inf 52.7%

       \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{a}\right)} \]
   13. Step-by-step derivation

       1. mul-1-neg 52.7%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{y}{a}\right)}\right) \]

       2. unsub-neg 52.7%

          \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y}{a}\right)} \]

   14. Simplified 52.7%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 39.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+70}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.5e+70) t (if (<= z 2.05e-22) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e+70) {
		tmp = t;
	} else if (z <= 2.05e-22) {
		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 <= (-3.5d+70)) then
        tmp = t
    else if (z <= 2.05d-22) 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 <= -3.5e+70) {
		tmp = t;
	} else if (z <= 2.05e-22) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.5e+70:
		tmp = t
	elif z <= 2.05e-22:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.5e+70)
		tmp = t;
	elseif (z <= 2.05e-22)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.5e+70)
		tmp = t;
	elseif (z <= 2.05e-22)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.5e+70], t, If[LessEqual[z, 2.05e-22], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -3.50000000000000002e70 or 2.05e-22 < z

   1. Initial program 49.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 49.2%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. *-commutative 49.2%

         \[\leadsto \frac{\color{blue}{\left(t - x\right) \cdot \left(y - z\right)}}{a - z} + x \]

      3. associate-/l* 77.2%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} + x \]

      4. fma-define 77.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]

   3. Simplified 77.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 34.8%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 34.8%

         \[\leadsto x + \color{blue}{\left(-\frac{z \cdot \left(t - x\right)}{a - z}\right)} \]

      2. associate-/l* 42.3%

         \[\leadsto x + \left(-\color{blue}{z \cdot \frac{t - x}{a - z}}\right) \]

      3. distribute-lft-neg-out 42.3%

         \[\leadsto x + \color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z}} \]

      4. +-commutative 42.3%

         \[\leadsto \color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z} + x} \]

      5. *-commutative 42.3%

         \[\leadsto \color{blue}{\frac{t - x}{a - z} \cdot \left(-z\right)} + x \]

      6. fma-define 42.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, -z, x\right)} \]

   7. Simplified 42.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, -z, x\right)} \]

   8. Taylor expanded in a around 0 46.6%

      \[\leadsto \color{blue}{t} \]

   if -3.50000000000000002e70 < z < 2.05e-22

   1. Initial program 85.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. +-commutative 85.0%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

      2. *-commutative 85.0%

         \[\leadsto \frac{\color{blue}{\left(t - x\right) \cdot \left(y - z\right)}}{a - z} + x \]

      3. associate-/l* 93.9%

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} + x \]

      4. fma-define 93.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]

   3. Simplified 93.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 36.4%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 25.0% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return t;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = t
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return t;
}

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 69.9%

   \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
2. Step-by-step derivation

   1. +-commutative 69.9%

      \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]

   2. *-commutative 69.9%

      \[\leadsto \frac{\color{blue}{\left(t - x\right) \cdot \left(y - z\right)}}{a - z} + x \]

   3. associate-/l* 86.8%

      \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} + x \]

   4. fma-define 86.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]

3. Simplified 86.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 40.7%

   \[\leadsto \color{blue}{x + -1 \cdot \frac{z \cdot \left(t - x\right)}{a - z}} \]
6. Step-by-step derivation

   1. mul-1-neg 40.7%

      \[\leadsto x + \color{blue}{\left(-\frac{z \cdot \left(t - x\right)}{a - z}\right)} \]

   2. associate-/l* 45.4%

      \[\leadsto x + \left(-\color{blue}{z \cdot \frac{t - x}{a - z}}\right) \]

   3. distribute-lft-neg-out 45.4%

      \[\leadsto x + \color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z}} \]

   4. +-commutative 45.4%

      \[\leadsto \color{blue}{\left(-z\right) \cdot \frac{t - x}{a - z} + x} \]

   5. *-commutative 45.4%

      \[\leadsto \color{blue}{\frac{t - x}{a - z} \cdot \left(-z\right)} + x \]

   6. fma-define 45.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, -z, x\right)} \]

7. Simplified 45.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, -z, x\right)} \]

8. Taylor expanded in a around 0 24.5%

   \[\leadsto \color{blue}{t} \]
9. Add Preprocessing

Developer Target 1: 84.4% 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 2024163 
(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))))