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

Percentage Accurate: 68.0% → 85.4%

Time: 17.1s

Alternatives: 20

Speedup: 0.8×

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: 68.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 85.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+295}\right):\\ \;\;\;\;t - \frac{y - a}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x \cdot \left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+295)))
     (- t (/ (- y a) (/ z (- t x))))
     (+
      (/ (* (- y z) t) (- a z))
      (* x (- (+ (/ z (- a z)) 1.0) (/ y (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+295)) {
		tmp = t - ((y - a) / (z / (t - x)));
	} else {
		tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0) - (y / (a - z))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+295)) {
		tmp = t - ((y - a) / (z / (t - x)));
	} else {
		tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0) - (y / (a - 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 <= -math.inf) or not (t_1 <= 5e+295):
		tmp = t - ((y - a) / (z / (t - x)))
	else:
		tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0) - (y / (a - z))))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+295))
		tmp = Float64(t - Float64(Float64(y - a) / Float64(z / Float64(t - x))));
	else
		tmp = Float64(Float64(Float64(Float64(y - z) * t) / Float64(a - z)) + Float64(x * Float64(Float64(Float64(z / Float64(a - z)) + 1.0) - Float64(y / Float64(a - 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 <= -Inf) || ~((t_1 <= 5e+295)))
		tmp = t - ((y - a) / (z / (t - x)));
	else
		tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0) - (y / (a - 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, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+295]], $MachinePrecision]], N[(t - N[(N[(y - a), $MachinePrecision] / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] - N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -inf.0 or 4.99999999999999991e295 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 38.8%

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

      1. +-commutative 38.8%

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

      2. associate-*l/ 73.3%

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

      3. fma-def 73.3%

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

   3. Simplified 73.3%

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

   4. Taylor expanded in z around inf 51.6%

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

      1. +-commutative 51.6%

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

      2. associate-/l* 80.0%

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

      3. distribute-lft-out-- 80.0%

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

      4. mul-1-neg 80.0%

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

      5. distribute-neg-frac 80.0%

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

      6. associate-/l* 51.6%

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

      7. *-commutative 51.6%

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

      8. distribute-rgt-out-- 51.3%

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

      9. unsub-neg 51.3%

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

      10. distribute-rgt-out-- 51.6%

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

      11. *-commutative 51.6%

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

      12. associate-/l* 80.0%

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

   6. Simplified 80.0%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 4.99999999999999991e295

   1. Initial program 84.3%

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

      1. +-commutative 84.3%

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

      2. associate-*l/ 81.6%

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

      3. fma-def 81.6%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in x around -inf 94.9%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -\infty \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 5 \cdot 10^{+295}\right):\\ \;\;\;\;t - \frac{y - a}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x \cdot \left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right)\\ \end{array} \]

Alternative 2: 51.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -6.8 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-116}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 34000:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+155}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a t)))))
   (if (<= a -6.8e+75)
     t_1
     (if (<= a 4.7e-116)
       (- t (* t (/ y z)))
       (if (<= a 34000.0)
         (/ y (/ z x))
         (if (<= a 2.55e+63)
           (* x (- 1.0 (/ y a)))
           (if (<= a 5.2e+83)
             (* y (/ x z))
             (if (<= a 8.6e+155) (+ x t) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double tmp;
	if (a <= -6.8e+75) {
		tmp = t_1;
	} else if (a <= 4.7e-116) {
		tmp = t - (t * (y / z));
	} else if (a <= 34000.0) {
		tmp = y / (z / x);
	} else if (a <= 2.55e+63) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= 5.2e+83) {
		tmp = y * (x / z);
	} else if (a <= 8.6e+155) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / t))
    if (a <= (-6.8d+75)) then
        tmp = t_1
    else if (a <= 4.7d-116) then
        tmp = t - (t * (y / z))
    else if (a <= 34000.0d0) then
        tmp = y / (z / x)
    else if (a <= 2.55d+63) then
        tmp = x * (1.0d0 - (y / a))
    else if (a <= 5.2d+83) then
        tmp = y * (x / z)
    else if (a <= 8.6d+155) then
        tmp = x + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double tmp;
	if (a <= -6.8e+75) {
		tmp = t_1;
	} else if (a <= 4.7e-116) {
		tmp = t - (t * (y / z));
	} else if (a <= 34000.0) {
		tmp = y / (z / x);
	} else if (a <= 2.55e+63) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= 5.2e+83) {
		tmp = y * (x / z);
	} else if (a <= 8.6e+155) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / t))
	tmp = 0
	if a <= -6.8e+75:
		tmp = t_1
	elif a <= 4.7e-116:
		tmp = t - (t * (y / z))
	elif a <= 34000.0:
		tmp = y / (z / x)
	elif a <= 2.55e+63:
		tmp = x * (1.0 - (y / a))
	elif a <= 5.2e+83:
		tmp = y * (x / z)
	elif a <= 8.6e+155:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / t)))
	tmp = 0.0
	if (a <= -6.8e+75)
		tmp = t_1;
	elseif (a <= 4.7e-116)
		tmp = Float64(t - Float64(t * Float64(y / z)));
	elseif (a <= 34000.0)
		tmp = Float64(y / Float64(z / x));
	elseif (a <= 2.55e+63)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (a <= 5.2e+83)
		tmp = Float64(y * Float64(x / z));
	elseif (a <= 8.6e+155)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / t));
	tmp = 0.0;
	if (a <= -6.8e+75)
		tmp = t_1;
	elseif (a <= 4.7e-116)
		tmp = t - (t * (y / z));
	elseif (a <= 34000.0)
		tmp = y / (z / x);
	elseif (a <= 2.55e+63)
		tmp = x * (1.0 - (y / a));
	elseif (a <= 5.2e+83)
		tmp = y * (x / z);
	elseif (a <= 8.6e+155)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.8e+75], t$95$1, If[LessEqual[a, 4.7e-116], N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 34000.0], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.55e+63], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e+83], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.6e+155], N[(x + t), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -6.80000000000000022e75 or 8.6000000000000005e155 < a

   1. Initial program 74.5%

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

      1. +-commutative 74.5%

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

      2. associate-*l/ 88.2%

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

      3. fma-def 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in z around 0 71.1%

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

      1. +-commutative 71.1%

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

      2. associate-/l* 77.8%

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

   6. Simplified 77.8%

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

   7. Taylor expanded in t around inf 72.2%

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

   if -6.80000000000000022e75 < a < 4.69999999999999994e-116

   1. Initial program 63.7%

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

      1. +-commutative 63.7%

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

      2. associate-*l/ 70.8%

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

      3. fma-def 70.9%

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

   3. Simplified 70.9%

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

   4. Taylor expanded in z around -inf 77.8%

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

   5. Taylor expanded in a around 0 74.6%

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

      1. mul-1-neg 74.6%

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

      2. unsub-neg 74.6%

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

      3. associate-/l* 76.9%

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

   7. Simplified 76.9%

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

   8. Taylor expanded in t around inf 59.0%

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

      1. associate-*l/ 59.8%

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

      2. *-commutative 59.8%

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

   10. Simplified 59.8%

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

   if 4.69999999999999994e-116 < a < 34000

   1. Initial program 61.3%

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

      1. +-commutative 61.3%

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

      2. associate-*l/ 71.8%

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

      3. fma-def 71.8%

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

   3. Simplified 71.8%

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

   4. Taylor expanded in y around -inf 52.7%

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

   5. Taylor expanded in t around 0 36.2%

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

      1. mul-1-neg 36.2%

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

      2. distribute-rgt-neg-in 36.2%

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

   7. Simplified 36.2%

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

   8. Taylor expanded in a around 0 35.7%

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

      1. associate-/l* 50.2%

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

   10. Simplified 50.2%

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

   if 34000 < a < 2.5499999999999999e63

   1. Initial program 92.1%

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

      1. associate-*l/ 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in z around 0 83.7%

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

   5. Taylor expanded in x around inf 67.8%

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

      1. *-commutative 67.8%

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

      2. mul-1-neg 67.8%

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

      3. unsub-neg 67.8%

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

   7. Simplified 67.8%

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

   if 2.5499999999999999e63 < a < 5.2000000000000002e83

   1. Initial program 35.1%

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

      1. +-commutative 35.1%

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

      2. associate-*l/ 67.0%

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

      3. fma-def 67.0%

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

   3. Simplified 67.0%

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

   4. Taylor expanded in y around -inf 36.4%

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

   5. Taylor expanded in t around 0 3.0%

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

      1. mul-1-neg 3.0%

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

      2. distribute-rgt-neg-in 3.0%

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

   7. Simplified 3.0%

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

   8. Taylor expanded in a around 0 3.0%

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

      1. associate-/l* 66.1%

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

   10. Simplified 66.1%

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

   11. Taylor expanded in y around 0 3.0%

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

       1. associate-*r/ 66.7%

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

   13. Simplified 66.7%

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

   if 5.2000000000000002e83 < a < 8.6000000000000005e155

   1. Initial program 72.1%

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

      1. +-commutative 72.1%

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

      2. associate-*l/ 92.5%

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

      3. fma-def 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in x around -inf 72.1%

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

   5. Taylor expanded in z around inf 70.2%

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

   6. Taylor expanded in a around inf 58.0%

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

      1. mul-1-neg 58.0%

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

   8. Simplified 58.0%

      \[\leadsto t + -1 \cdot \color{blue}{\left(-x\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-116}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 34000:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+155}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 3: 37.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{+32}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -510000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{-117}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5400000:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.6e+75)
   x
   (if (<= a -2.8e+32)
     t
     (if (<= a -510000000.0)
       x
       (if (<= a -4.1e-50)
         (* x (/ y z))
         (if (<= a 3.05e-117) t (if (<= a 5400000.0) (* y (/ x z)) x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.6e+75) {
		tmp = x;
	} else if (a <= -2.8e+32) {
		tmp = t;
	} else if (a <= -510000000.0) {
		tmp = x;
	} else if (a <= -4.1e-50) {
		tmp = x * (y / z);
	} else if (a <= 3.05e-117) {
		tmp = t;
	} else if (a <= 5400000.0) {
		tmp = y * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.6d+75)) then
        tmp = x
    else if (a <= (-2.8d+32)) then
        tmp = t
    else if (a <= (-510000000.0d0)) then
        tmp = x
    else if (a <= (-4.1d-50)) then
        tmp = x * (y / z)
    else if (a <= 3.05d-117) then
        tmp = t
    else if (a <= 5400000.0d0) then
        tmp = y * (x / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.6e+75) {
		tmp = x;
	} else if (a <= -2.8e+32) {
		tmp = t;
	} else if (a <= -510000000.0) {
		tmp = x;
	} else if (a <= -4.1e-50) {
		tmp = x * (y / z);
	} else if (a <= 3.05e-117) {
		tmp = t;
	} else if (a <= 5400000.0) {
		tmp = y * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.6e+75:
		tmp = x
	elif a <= -2.8e+32:
		tmp = t
	elif a <= -510000000.0:
		tmp = x
	elif a <= -4.1e-50:
		tmp = x * (y / z)
	elif a <= 3.05e-117:
		tmp = t
	elif a <= 5400000.0:
		tmp = y * (x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.6e+75)
		tmp = x;
	elseif (a <= -2.8e+32)
		tmp = t;
	elseif (a <= -510000000.0)
		tmp = x;
	elseif (a <= -4.1e-50)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 3.05e-117)
		tmp = t;
	elseif (a <= 5400000.0)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.6e+75)
		tmp = x;
	elseif (a <= -2.8e+32)
		tmp = t;
	elseif (a <= -510000000.0)
		tmp = x;
	elseif (a <= -4.1e-50)
		tmp = x * (y / z);
	elseif (a <= 3.05e-117)
		tmp = t;
	elseif (a <= 5400000.0)
		tmp = y * (x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.6e+75], x, If[LessEqual[a, -2.8e+32], t, If[LessEqual[a, -510000000.0], x, If[LessEqual[a, -4.1e-50], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.05e-117], t, If[LessEqual[a, 5400000.0], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.60000000000000023e75 or -2.8e32 < a < -5.1e8 or 5.4e6 < a

   1. Initial program 75.7%

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

      1. +-commutative 75.7%

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

      2. associate-*l/ 88.8%

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

      3. fma-def 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in a around inf 49.7%

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

   if -5.60000000000000023e75 < a < -2.8e32 or -4.09999999999999985e-50 < a < 3.05000000000000001e-117

   1. Initial program 62.9%

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

      1. +-commutative 62.9%

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

      2. associate-*l/ 70.0%

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

      3. fma-def 70.0%

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

   3. Simplified 70.0%

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

   4. Taylor expanded in z around inf 45.6%

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

   if -5.1e8 < a < -4.09999999999999985e-50

   1. Initial program 61.8%

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

      1. +-commutative 61.8%

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

      2. associate-*l/ 70.2%

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

      3. fma-def 70.7%

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

   3. Simplified 70.7%

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

   4. Taylor expanded in y around -inf 48.9%

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

   5. Taylor expanded in t around 0 30.8%

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

      1. mul-1-neg 30.8%

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

      2. distribute-rgt-neg-in 30.8%

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

   7. Simplified 30.8%

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

   8. Taylor expanded in a around 0 31.0%

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

      1. associate-/l* 39.1%

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

   10. Simplified 39.1%

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

       1. associate-/r/ 47.6%

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

   12. Applied egg-rr 47.6%

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

   if 3.05000000000000001e-117 < a < 5.4e6

   1. Initial program 61.3%

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

      1. +-commutative 61.3%

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

      2. associate-*l/ 71.8%

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

      3. fma-def 71.8%

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

   3. Simplified 71.8%

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

   4. Taylor expanded in y around -inf 52.7%

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

   5. Taylor expanded in t around 0 36.2%

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

      1. mul-1-neg 36.2%

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

      2. distribute-rgt-neg-in 36.2%

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

   7. Simplified 36.2%

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

   8. Taylor expanded in a around 0 35.7%

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

      1. associate-/l* 50.2%

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

   10. Simplified 50.2%

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

   11. Taylor expanded in y around 0 35.7%

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

       1. associate-*r/ 50.1%

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

   13. Simplified 50.1%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{+32}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -510000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{-117}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5400000:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 37.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{+32}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -850000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-118}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 43000:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.2e+75)
   x
   (if (<= a -4.5e+32)
     t
     (if (<= a -850000000.0)
       x
       (if (<= a -2.3e-52)
         (* x (/ y z))
         (if (<= a 9e-118) t (if (<= a 43000.0) (/ y (/ z x)) x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.2e+75) {
		tmp = x;
	} else if (a <= -4.5e+32) {
		tmp = t;
	} else if (a <= -850000000.0) {
		tmp = x;
	} else if (a <= -2.3e-52) {
		tmp = x * (y / z);
	} else if (a <= 9e-118) {
		tmp = t;
	} else if (a <= 43000.0) {
		tmp = y / (z / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.2d+75)) then
        tmp = x
    else if (a <= (-4.5d+32)) then
        tmp = t
    else if (a <= (-850000000.0d0)) then
        tmp = x
    else if (a <= (-2.3d-52)) then
        tmp = x * (y / z)
    else if (a <= 9d-118) then
        tmp = t
    else if (a <= 43000.0d0) then
        tmp = y / (z / x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.2e+75) {
		tmp = x;
	} else if (a <= -4.5e+32) {
		tmp = t;
	} else if (a <= -850000000.0) {
		tmp = x;
	} else if (a <= -2.3e-52) {
		tmp = x * (y / z);
	} else if (a <= 9e-118) {
		tmp = t;
	} else if (a <= 43000.0) {
		tmp = y / (z / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.2e+75:
		tmp = x
	elif a <= -4.5e+32:
		tmp = t
	elif a <= -850000000.0:
		tmp = x
	elif a <= -2.3e-52:
		tmp = x * (y / z)
	elif a <= 9e-118:
		tmp = t
	elif a <= 43000.0:
		tmp = y / (z / x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.2e+75)
		tmp = x;
	elseif (a <= -4.5e+32)
		tmp = t;
	elseif (a <= -850000000.0)
		tmp = x;
	elseif (a <= -2.3e-52)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 9e-118)
		tmp = t;
	elseif (a <= 43000.0)
		tmp = Float64(y / Float64(z / x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.2e+75)
		tmp = x;
	elseif (a <= -4.5e+32)
		tmp = t;
	elseif (a <= -850000000.0)
		tmp = x;
	elseif (a <= -2.3e-52)
		tmp = x * (y / z);
	elseif (a <= 9e-118)
		tmp = t;
	elseif (a <= 43000.0)
		tmp = y / (z / x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.2e+75], x, If[LessEqual[a, -4.5e+32], t, If[LessEqual[a, -850000000.0], x, If[LessEqual[a, -2.3e-52], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e-118], t, If[LessEqual[a, 43000.0], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.2000000000000002e75 or -4.5000000000000003e32 < a < -8.5e8 or 43000 < a

   1. Initial program 75.7%

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

      1. +-commutative 75.7%

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

      2. associate-*l/ 88.8%

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

      3. fma-def 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in a around inf 49.7%

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

   if -6.2000000000000002e75 < a < -4.5000000000000003e32 or -2.29999999999999994e-52 < a < 9.0000000000000001e-118

   1. Initial program 62.9%

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

      1. +-commutative 62.9%

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

      2. associate-*l/ 70.0%

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

      3. fma-def 70.0%

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

   3. Simplified 70.0%

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

   4. Taylor expanded in z around inf 45.6%

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

   if -8.5e8 < a < -2.29999999999999994e-52

   1. Initial program 61.8%

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

      1. +-commutative 61.8%

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

      2. associate-*l/ 70.2%

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

      3. fma-def 70.7%

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

   3. Simplified 70.7%

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

   4. Taylor expanded in y around -inf 48.9%

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

   5. Taylor expanded in t around 0 30.8%

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

      1. mul-1-neg 30.8%

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

      2. distribute-rgt-neg-in 30.8%

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

   7. Simplified 30.8%

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

   8. Taylor expanded in a around 0 31.0%

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

      1. associate-/l* 39.1%

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

   10. Simplified 39.1%

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

       1. associate-/r/ 47.6%

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

   12. Applied egg-rr 47.6%

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

   if 9.0000000000000001e-118 < a < 43000

   1. Initial program 61.3%

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

      1. +-commutative 61.3%

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

      2. associate-*l/ 71.8%

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

      3. fma-def 71.8%

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

   3. Simplified 71.8%

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

   4. Taylor expanded in y around -inf 52.7%

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

   5. Taylor expanded in t around 0 36.2%

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

      1. mul-1-neg 36.2%

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

      2. distribute-rgt-neg-in 36.2%

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

   7. Simplified 36.2%

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

   8. Taylor expanded in a around 0 35.7%

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

      1. associate-/l* 50.2%

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

   10. Simplified 50.2%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{+32}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -850000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-118}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 43000:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 57.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+29}:\\ \;\;\;\;t - y \cdot \frac{x}{-z}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a t)))))
   (if (<= a -6.5e+75)
     t_1
     (if (<= a 5.2e+29)
       (- t (* y (/ x (- z))))
       (if (<= a 8.8e+128)
         (* x (- 1.0 (/ y a)))
         (if (<= a 1.55e+156) (* t (/ (- y z) (- a z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double tmp;
	if (a <= -6.5e+75) {
		tmp = t_1;
	} else if (a <= 5.2e+29) {
		tmp = t - (y * (x / -z));
	} else if (a <= 8.8e+128) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= 1.55e+156) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / t))
    if (a <= (-6.5d+75)) then
        tmp = t_1
    else if (a <= 5.2d+29) then
        tmp = t - (y * (x / -z))
    else if (a <= 8.8d+128) then
        tmp = x * (1.0d0 - (y / a))
    else if (a <= 1.55d+156) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double tmp;
	if (a <= -6.5e+75) {
		tmp = t_1;
	} else if (a <= 5.2e+29) {
		tmp = t - (y * (x / -z));
	} else if (a <= 8.8e+128) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= 1.55e+156) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / t))
	tmp = 0
	if a <= -6.5e+75:
		tmp = t_1
	elif a <= 5.2e+29:
		tmp = t - (y * (x / -z))
	elif a <= 8.8e+128:
		tmp = x * (1.0 - (y / a))
	elif a <= 1.55e+156:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / t)))
	tmp = 0.0
	if (a <= -6.5e+75)
		tmp = t_1;
	elseif (a <= 5.2e+29)
		tmp = Float64(t - Float64(y * Float64(x / Float64(-z))));
	elseif (a <= 8.8e+128)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (a <= 1.55e+156)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / t));
	tmp = 0.0;
	if (a <= -6.5e+75)
		tmp = t_1;
	elseif (a <= 5.2e+29)
		tmp = t - (y * (x / -z));
	elseif (a <= 8.8e+128)
		tmp = x * (1.0 - (y / a));
	elseif (a <= 1.55e+156)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.5e+75], t$95$1, If[LessEqual[a, 5.2e+29], N[(t - N[(y * N[(x / (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.8e+128], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e+156], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.4999999999999998e75 or 1.5500000000000001e156 < a

   1. Initial program 74.5%

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

      1. +-commutative 74.5%

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

      2. associate-*l/ 88.2%

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

      3. fma-def 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in z around 0 71.1%

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

      1. +-commutative 71.1%

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

      2. associate-/l* 77.8%

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

   6. Simplified 77.8%

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

   7. Taylor expanded in t around inf 72.2%

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

   if -6.4999999999999998e75 < a < 5.2e29

   1. Initial program 63.6%

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

      1. +-commutative 63.6%

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

      2. associate-*l/ 71.1%

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

      3. fma-def 71.2%

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

   3. Simplified 71.2%

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

   4. Taylor expanded in z around -inf 72.9%

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

   5. Taylor expanded in a around 0 70.4%

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

      1. mul-1-neg 70.4%

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

      2. unsub-neg 70.4%

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

      3. associate-/l* 75.5%

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

   7. Simplified 75.5%

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

   8. Taylor expanded in t around 0 57.1%

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

      1. associate-/l* 61.6%

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

      2. associate-*r/ 61.6%

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

      3. *-commutative 61.6%

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

      4. associate-*l/ 61.6%

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

      5. metadata-eval 61.6%

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

      6. times-frac 61.6%

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

      7. *-commutative 61.6%

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

      8. associate-*r/ 61.6%

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

      9. mul-1-neg 61.6%

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

      10. distribute-frac-neg 61.6%

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

      11. associate-/r/ 61.6%

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

      12. associate-*l/ 61.6%

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

      13. *-lft-identity 61.6%

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

   10. Simplified 61.6%

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

   if 5.2e29 < a < 8.80000000000000066e128

   1. Initial program 84.1%

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

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in z around 0 78.3%

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

   5. Taylor expanded in x around inf 67.7%

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

      1. *-commutative 67.7%

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

      2. mul-1-neg 67.7%

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

      3. unsub-neg 67.7%

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

   7. Simplified 67.7%

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

   if 8.80000000000000066e128 < a < 1.5500000000000001e156

   1. Initial program 54.8%

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

      1. +-commutative 54.8%

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

      2. associate-*l/ 83.7%

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

      3. fma-def 83.7%

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

   3. Simplified 83.7%

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

   4. Taylor expanded in t around inf 100.0%

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

      1. div-sub 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+29}:\\ \;\;\;\;t - y \cdot \frac{x}{-z}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 6: 68.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 370000000000:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+129}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 10^{+156}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a (- t x))))))
   (if (<= a -5.6e+75)
     t_1
     (if (<= a 370000000000.0)
       (- t (/ y (/ z (- t x))))
       (if (<= a 2.6e+129)
         (+ x (* (- t x) (/ y a)))
         (if (<= a 1e+156) (* t (/ (- y z) (- a z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double tmp;
	if (a <= -5.6e+75) {
		tmp = t_1;
	} else if (a <= 370000000000.0) {
		tmp = t - (y / (z / (t - x)));
	} else if (a <= 2.6e+129) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 1e+156) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / (t - x)))
    if (a <= (-5.6d+75)) then
        tmp = t_1
    else if (a <= 370000000000.0d0) then
        tmp = t - (y / (z / (t - x)))
    else if (a <= 2.6d+129) then
        tmp = x + ((t - x) * (y / a))
    else if (a <= 1d+156) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double tmp;
	if (a <= -5.6e+75) {
		tmp = t_1;
	} else if (a <= 370000000000.0) {
		tmp = t - (y / (z / (t - x)));
	} else if (a <= 2.6e+129) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 1e+156) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / (t - x)))
	tmp = 0
	if a <= -5.6e+75:
		tmp = t_1
	elif a <= 370000000000.0:
		tmp = t - (y / (z / (t - x)))
	elif a <= 2.6e+129:
		tmp = x + ((t - x) * (y / a))
	elif a <= 1e+156:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / Float64(t - x))))
	tmp = 0.0
	if (a <= -5.6e+75)
		tmp = t_1;
	elseif (a <= 370000000000.0)
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	elseif (a <= 2.6e+129)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (a <= 1e+156)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / (t - x)));
	tmp = 0.0;
	if (a <= -5.6e+75)
		tmp = t_1;
	elseif (a <= 370000000000.0)
		tmp = t - (y / (z / (t - x)));
	elseif (a <= 2.6e+129)
		tmp = x + ((t - x) * (y / a));
	elseif (a <= 1e+156)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.6e+75], t$95$1, If[LessEqual[a, 370000000000.0], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e+129], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e+156], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.60000000000000023e75 or 9.9999999999999998e155 < a

   1. Initial program 74.5%

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

      1. +-commutative 74.5%

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

      2. associate-*l/ 88.2%

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

      3. fma-def 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in z around 0 71.1%

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

      1. +-commutative 71.1%

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

      2. associate-/l* 77.8%

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

   6. Simplified 77.8%

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

   if -5.60000000000000023e75 < a < 3.7e11

   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. associate-*l/ 71.0%

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

      3. fma-def 71.0%

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

   3. Simplified 71.0%

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

   4. Taylor expanded in z around -inf 74.3%

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

   5. Taylor expanded in a around 0 71.6%

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

      1. mul-1-neg 71.6%

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

      2. unsub-neg 71.6%

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

      3. associate-/l* 76.8%

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

   7. Simplified 76.8%

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

   if 3.7e11 < a < 2.60000000000000012e129

   1. Initial program 82.7%

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

      1. associate-*l/ 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in z around 0 73.4%

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

   if 2.60000000000000012e129 < a < 9.9999999999999998e155

   1. Initial program 54.8%

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

      1. +-commutative 54.8%

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

      2. associate-*l/ 83.7%

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

      3. fma-def 83.7%

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

   3. Simplified 83.7%

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

   4. Taylor expanded in t around inf 100.0%

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

      1. div-sub 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 370000000000:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+129}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 10^{+156}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 7: 70.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+14}:\\ \;\;\;\;t - \frac{y - a}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+129}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 10^{+156}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a (- t x))))))
   (if (<= a -5.6e+75)
     t_1
     (if (<= a 1.35e+14)
       (- t (/ (- y a) (/ z (- t x))))
       (if (<= a 1.65e+129)
         (+ x (* (- t x) (/ y a)))
         (if (<= a 1e+156) (* t (/ (- y z) (- a z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double tmp;
	if (a <= -5.6e+75) {
		tmp = t_1;
	} else if (a <= 1.35e+14) {
		tmp = t - ((y - a) / (z / (t - x)));
	} else if (a <= 1.65e+129) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 1e+156) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / (t - x)))
    if (a <= (-5.6d+75)) then
        tmp = t_1
    else if (a <= 1.35d+14) then
        tmp = t - ((y - a) / (z / (t - x)))
    else if (a <= 1.65d+129) then
        tmp = x + ((t - x) * (y / a))
    else if (a <= 1d+156) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double tmp;
	if (a <= -5.6e+75) {
		tmp = t_1;
	} else if (a <= 1.35e+14) {
		tmp = t - ((y - a) / (z / (t - x)));
	} else if (a <= 1.65e+129) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 1e+156) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / (t - x)))
	tmp = 0
	if a <= -5.6e+75:
		tmp = t_1
	elif a <= 1.35e+14:
		tmp = t - ((y - a) / (z / (t - x)))
	elif a <= 1.65e+129:
		tmp = x + ((t - x) * (y / a))
	elif a <= 1e+156:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / Float64(t - x))))
	tmp = 0.0
	if (a <= -5.6e+75)
		tmp = t_1;
	elseif (a <= 1.35e+14)
		tmp = Float64(t - Float64(Float64(y - a) / Float64(z / Float64(t - x))));
	elseif (a <= 1.65e+129)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (a <= 1e+156)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / (t - x)));
	tmp = 0.0;
	if (a <= -5.6e+75)
		tmp = t_1;
	elseif (a <= 1.35e+14)
		tmp = t - ((y - a) / (z / (t - x)));
	elseif (a <= 1.65e+129)
		tmp = x + ((t - x) * (y / a));
	elseif (a <= 1e+156)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.6e+75], t$95$1, If[LessEqual[a, 1.35e+14], N[(t - N[(N[(y - a), $MachinePrecision] / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e+129], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e+156], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.60000000000000023e75 or 9.9999999999999998e155 < a

   1. Initial program 74.5%

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

      1. +-commutative 74.5%

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

      2. associate-*l/ 88.2%

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

      3. fma-def 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in z around 0 71.1%

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

      1. +-commutative 71.1%

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

      2. associate-/l* 77.8%

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

   6. Simplified 77.8%

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

   if -5.60000000000000023e75 < a < 1.35e14

   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. associate-*l/ 71.0%

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

      3. fma-def 71.0%

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

   3. Simplified 71.0%

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

   4. Taylor expanded in z around inf 74.3%

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

      1. +-commutative 74.3%

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

      2. associate-/l* 80.8%

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

      3. distribute-lft-out-- 80.8%

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

      4. mul-1-neg 80.8%

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

      5. distribute-neg-frac 80.8%

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

      6. associate-/l* 74.3%

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

      7. *-commutative 74.3%

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

      8. distribute-rgt-out-- 74.3%

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

      9. unsub-neg 74.3%

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

      10. distribute-rgt-out-- 74.3%

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

      11. *-commutative 74.3%

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

      12. associate-/l* 80.8%

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

   6. Simplified 80.8%

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

   if 1.35e14 < a < 1.64999999999999995e129

   1. Initial program 82.7%

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

      1. associate-*l/ 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in z around 0 73.4%

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

   if 1.64999999999999995e129 < a < 9.9999999999999998e155

   1. Initial program 54.8%

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

      1. +-commutative 54.8%

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

      2. associate-*l/ 83.7%

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

      3. fma-def 83.7%

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

   3. Simplified 83.7%

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

   4. Taylor expanded in t around inf 100.0%

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

      1. div-sub 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+14}:\\ \;\;\;\;t - \frac{y - a}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+129}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 10^{+156}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 8: 88.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+177} \lor \neg \left(z \leq 4.5 \cdot 10^{+130}\right):\\ \;\;\;\;t - \frac{y - a}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.15e+177) (not (<= z 4.5e+130)))
   (- t (/ (- y a) (/ z (- t x))))
   (+ x (* (- t x) (/ (- y z) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.15e+177) || !(z <= 4.5e+130)) {
		tmp = t - ((y - a) / (z / (t - x)));
	} else {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.15d+177)) .or. (.not. (z <= 4.5d+130))) then
        tmp = t - ((y - a) / (z / (t - x)))
    else
        tmp = x + ((t - x) * ((y - z) / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.15e+177) || !(z <= 4.5e+130)) {
		tmp = t - ((y - a) / (z / (t - x)));
	} else {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.15e+177) or not (z <= 4.5e+130):
		tmp = t - ((y - a) / (z / (t - x)))
	else:
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.15e+177) || !(z <= 4.5e+130))
		tmp = Float64(t - Float64(Float64(y - a) / Float64(z / Float64(t - x))));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.15e+177) || ~((z <= 4.5e+130)))
		tmp = t - ((y - a) / (z / (t - x)));
	else
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.15e+177], N[Not[LessEqual[z, 4.5e+130]], $MachinePrecision]], N[(t - N[(N[(y - a), $MachinePrecision] / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.15e177 or 4.50000000000000039e130 < z

   1. Initial program 25.8%

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

      1. +-commutative 25.8%

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

      2. associate-*l/ 53.1%

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

      3. fma-def 53.1%

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

   3. Simplified 53.1%

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

   4. Taylor expanded in z around inf 59.1%

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

      1. +-commutative 59.1%

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

      2. associate-/l* 87.1%

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

      3. distribute-lft-out-- 87.1%

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

      4. mul-1-neg 87.1%

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

      5. distribute-neg-frac 87.1%

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

      6. associate-/l* 59.1%

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

      7. *-commutative 59.1%

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

      8. distribute-rgt-out-- 59.0%

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

      9. unsub-neg 59.0%

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

      10. distribute-rgt-out-- 59.1%

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

      11. *-commutative 59.1%

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

      12. associate-/l* 87.1%

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

   6. Simplified 87.1%

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

   if -3.15e177 < z < 4.50000000000000039e130

   1. Initial program 84.9%

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

      1. associate-*l/ 88.6%

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

   3. Simplified 88.6%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+177} \lor \neg \left(z \leq 4.5 \cdot 10^{+130}\right):\\ \;\;\;\;t - \frac{y - a}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 9: 66.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - y \cdot \frac{x}{-z}\\ \mathbf{if}\;z \leq -6 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-55}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+51}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* y (/ x (- z))))))
   (if (<= z -6e+18)
     t_1
     (if (<= z 4.9e-55)
       (+ x (* (- t x) (/ y a)))
       (if (<= z 5.0)
         (* t (/ (- y z) (- a z)))
         (if (<= z 1.3e+51) (- x (/ (* x y) a)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (y * (x / -z));
	double tmp;
	if (z <= -6e+18) {
		tmp = t_1;
	} else if (z <= 4.9e-55) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 5.0) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 1.3e+51) {
		tmp = x - ((x * 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 - (y * (x / -z))
    if (z <= (-6d+18)) then
        tmp = t_1
    else if (z <= 4.9d-55) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 5.0d0) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 1.3d+51) then
        tmp = x - ((x * 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 - (y * (x / -z));
	double tmp;
	if (z <= -6e+18) {
		tmp = t_1;
	} else if (z <= 4.9e-55) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 5.0) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 1.3e+51) {
		tmp = x - ((x * y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (y * (x / -z))
	tmp = 0
	if z <= -6e+18:
		tmp = t_1
	elif z <= 4.9e-55:
		tmp = x + ((t - x) * (y / a))
	elif z <= 5.0:
		tmp = t * ((y - z) / (a - z))
	elif z <= 1.3e+51:
		tmp = x - ((x * y) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(y * Float64(x / Float64(-z))))
	tmp = 0.0
	if (z <= -6e+18)
		tmp = t_1;
	elseif (z <= 4.9e-55)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 5.0)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 1.3e+51)
		tmp = Float64(x - Float64(Float64(x * y) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (y * (x / -z));
	tmp = 0.0;
	if (z <= -6e+18)
		tmp = t_1;
	elseif (z <= 4.9e-55)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 5.0)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 1.3e+51)
		tmp = x - ((x * 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[(y * N[(x / (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+18], t$95$1, If[LessEqual[z, 4.9e-55], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.0], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+51], N[(x - N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6e18 or 1.3000000000000001e51 < z

   1. Initial program 42.3%

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

      1. +-commutative 42.3%

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

      2. associate-*l/ 63.7%

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

      3. fma-def 63.6%

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

   3. Simplified 63.6%

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

   4. Taylor expanded in z around -inf 61.4%

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

   5. Taylor expanded in a around 0 58.7%

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

      1. mul-1-neg 58.7%

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

      2. unsub-neg 58.7%

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

      3. associate-/l* 69.5%

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

   7. Simplified 69.5%

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

   8. Taylor expanded in t around 0 54.5%

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

      1. associate-/l* 62.3%

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

      2. associate-*r/ 62.3%

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

      3. *-commutative 62.3%

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

      4. associate-*l/ 62.3%

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

      5. metadata-eval 62.3%

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

      6. times-frac 62.3%

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

      7. *-commutative 62.3%

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

      8. associate-*r/ 62.2%

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

      9. mul-1-neg 62.2%

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

      10. distribute-frac-neg 62.2%

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

      11. associate-/r/ 62.3%

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

      12. associate-*l/ 62.3%

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

      13. *-lft-identity 62.3%

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

   10. Simplified 62.3%

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

   if -6e18 < z < 4.90000000000000035e-55

   1. Initial program 93.7%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in z around 0 77.7%

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

   if 4.90000000000000035e-55 < z < 5

   1. Initial program 83.8%

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

      1. +-commutative 83.8%

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

      2. associate-*l/ 88.9%

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

      3. fma-def 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in t around inf 72.6%

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

      1. div-sub 72.6%

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

   6. Simplified 72.6%

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

   if 5 < z < 1.3000000000000001e51

   1. Initial program 93.5%

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

      1. associate-*l/ 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in z around 0 73.9%

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

   5. Taylor expanded in t around 0 74.1%

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

      1. +-commutative 74.1%

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

      2. mul-1-neg 74.1%

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

      3. unsub-neg 74.1%

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

   7. Simplified 74.1%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+18}:\\ \;\;\;\;t - y \cdot \frac{x}{-z}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-55}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+51}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \frac{x}{-z}\\ \end{array} \]

Alternative 10: 65.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - y \cdot \frac{x}{-z}\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-55}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 0.85:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+50}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* y (/ x (- z))))))
   (if (<= z -6.5e+18)
     t_1
     (if (<= z 3.6e-55)
       (+ x (/ y (/ a (- t x))))
       (if (<= z 0.85)
         (* t (/ (- y z) (- a z)))
         (if (<= z 9e+50) (- x (/ (* x y) a)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (y * (x / -z));
	double tmp;
	if (z <= -6.5e+18) {
		tmp = t_1;
	} else if (z <= 3.6e-55) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 0.85) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 9e+50) {
		tmp = x - ((x * 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 - (y * (x / -z))
    if (z <= (-6.5d+18)) then
        tmp = t_1
    else if (z <= 3.6d-55) then
        tmp = x + (y / (a / (t - x)))
    else if (z <= 0.85d0) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 9d+50) then
        tmp = x - ((x * 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 - (y * (x / -z));
	double tmp;
	if (z <= -6.5e+18) {
		tmp = t_1;
	} else if (z <= 3.6e-55) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 0.85) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 9e+50) {
		tmp = x - ((x * y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (y * (x / -z))
	tmp = 0
	if z <= -6.5e+18:
		tmp = t_1
	elif z <= 3.6e-55:
		tmp = x + (y / (a / (t - x)))
	elif z <= 0.85:
		tmp = t * ((y - z) / (a - z))
	elif z <= 9e+50:
		tmp = x - ((x * y) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(y * Float64(x / Float64(-z))))
	tmp = 0.0
	if (z <= -6.5e+18)
		tmp = t_1;
	elseif (z <= 3.6e-55)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (z <= 0.85)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 9e+50)
		tmp = Float64(x - Float64(Float64(x * y) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (y * (x / -z));
	tmp = 0.0;
	if (z <= -6.5e+18)
		tmp = t_1;
	elseif (z <= 3.6e-55)
		tmp = x + (y / (a / (t - x)));
	elseif (z <= 0.85)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 9e+50)
		tmp = x - ((x * 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[(y * N[(x / (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+18], t$95$1, If[LessEqual[z, 3.6e-55], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.85], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+50], N[(x - N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.5e18 or 9.00000000000000027e50 < z

   1. Initial program 42.3%

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

      1. +-commutative 42.3%

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

      2. associate-*l/ 63.7%

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

      3. fma-def 63.6%

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

   3. Simplified 63.6%

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

   4. Taylor expanded in z around -inf 61.4%

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

   5. Taylor expanded in a around 0 58.7%

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

      1. mul-1-neg 58.7%

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

      2. unsub-neg 58.7%

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

      3. associate-/l* 69.5%

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

   7. Simplified 69.5%

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

   8. Taylor expanded in t around 0 54.5%

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

      1. associate-/l* 62.3%

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

      2. associate-*r/ 62.3%

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

      3. *-commutative 62.3%

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

      4. associate-*l/ 62.3%

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

      5. metadata-eval 62.3%

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

      6. times-frac 62.3%

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

      7. *-commutative 62.3%

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

      8. associate-*r/ 62.2%

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

      9. mul-1-neg 62.2%

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

      10. distribute-frac-neg 62.2%

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

      11. associate-/r/ 62.3%

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

      12. associate-*l/ 62.3%

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

      13. *-lft-identity 62.3%

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

   10. Simplified 62.3%

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

   if -6.5e18 < z < 3.6000000000000001e-55

   1. Initial program 93.7%

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

      1. +-commutative 93.7%

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

      2. associate-*l/ 92.9%

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

      3. fma-def 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in z around 0 76.8%

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

      1. +-commutative 76.8%

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

      2. associate-/l* 77.7%

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

   6. Simplified 77.7%

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

   if 3.6000000000000001e-55 < z < 0.849999999999999978

   1. Initial program 83.8%

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

      1. +-commutative 83.8%

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

      2. associate-*l/ 88.9%

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

      3. fma-def 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in t around inf 72.6%

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

      1. div-sub 72.6%

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

   6. Simplified 72.6%

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

   if 0.849999999999999978 < z < 9.00000000000000027e50

   1. Initial program 93.5%

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

      1. associate-*l/ 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in z around 0 73.9%

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

   5. Taylor expanded in t around 0 74.1%

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

      1. +-commutative 74.1%

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

      2. mul-1-neg 74.1%

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

      3. unsub-neg 74.1%

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

   7. Simplified 74.1%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+18}:\\ \;\;\;\;t - y \cdot \frac{x}{-z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-55}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 0.85:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+50}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \frac{x}{-z}\\ \end{array} \]

Alternative 11: 46.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+202}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-6}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -8.5e+202)
     t
     (if (<= z 6.5e-56)
       t_1
       (if (<= z 4.2e-6) (+ x t) (if (<= z 3e+51) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -8.5e+202) {
		tmp = t;
	} else if (z <= 6.5e-56) {
		tmp = t_1;
	} else if (z <= 4.2e-6) {
		tmp = x + t;
	} else if (z <= 3e+51) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-8.5d+202)) then
        tmp = t
    else if (z <= 6.5d-56) then
        tmp = t_1
    else if (z <= 4.2d-6) then
        tmp = x + t
    else if (z <= 3d+51) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -8.5e+202) {
		tmp = t;
	} else if (z <= 6.5e-56) {
		tmp = t_1;
	} else if (z <= 4.2e-6) {
		tmp = x + t;
	} else if (z <= 3e+51) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -8.5e+202:
		tmp = t
	elif z <= 6.5e-56:
		tmp = t_1
	elif z <= 4.2e-6:
		tmp = x + t
	elif z <= 3e+51:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -8.5e+202)
		tmp = t;
	elseif (z <= 6.5e-56)
		tmp = t_1;
	elseif (z <= 4.2e-6)
		tmp = Float64(x + t);
	elseif (z <= 3e+51)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -8.5e+202)
		tmp = t;
	elseif (z <= 6.5e-56)
		tmp = t_1;
	elseif (z <= 4.2e-6)
		tmp = x + t;
	elseif (z <= 3e+51)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+202], t, If[LessEqual[z, 6.5e-56], t$95$1, If[LessEqual[z, 4.2e-6], N[(x + t), $MachinePrecision], If[LessEqual[z, 3e+51], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5000000000000003e202 or 3e51 < z

   1. Initial program 34.9%

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

      1. +-commutative 34.9%

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

      2. associate-*l/ 58.0%

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

      3. fma-def 58.0%

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

   3. Simplified 58.0%

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

   4. Taylor expanded in z around inf 49.3%

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

   if -8.5000000000000003e202 < z < 6.4999999999999997e-56 or 4.1999999999999996e-6 < z < 3e51

   1. Initial program 85.3%

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

      1. associate-*l/ 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in z around 0 65.8%

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

   5. Taylor expanded in x around inf 52.0%

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

      1. *-commutative 52.0%

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

      2. mul-1-neg 52.0%

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

      3. unsub-neg 52.0%

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

   7. Simplified 52.0%

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

   if 6.4999999999999997e-56 < z < 4.1999999999999996e-6

   1. Initial program 87.7%

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

      1. +-commutative 87.7%

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

      2. associate-*l/ 87.7%

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

      3. fma-def 87.7%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in x around -inf 97.1%

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

   5. Taylor expanded in z around inf 63.4%

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

   6. Taylor expanded in a around inf 49.8%

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

      1. mul-1-neg 49.8%

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

   8. Simplified 49.8%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+202}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-6}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 58.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-135}:\\ \;\;\;\;t - y \cdot \frac{x}{-z}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+92}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a t)))))
   (if (<= a -5.6e+75)
     t_1
     (if (<= a 1.85e-135)
       (- t (* y (/ x (- z))))
       (if (<= a 1.5e+92) (* y (/ (- t x) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double tmp;
	if (a <= -5.6e+75) {
		tmp = t_1;
	} else if (a <= 1.85e-135) {
		tmp = t - (y * (x / -z));
	} else if (a <= 1.5e+92) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / t))
    if (a <= (-5.6d+75)) then
        tmp = t_1
    else if (a <= 1.85d-135) then
        tmp = t - (y * (x / -z))
    else if (a <= 1.5d+92) then
        tmp = y * ((t - x) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double tmp;
	if (a <= -5.6e+75) {
		tmp = t_1;
	} else if (a <= 1.85e-135) {
		tmp = t - (y * (x / -z));
	} else if (a <= 1.5e+92) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / t))
	tmp = 0
	if a <= -5.6e+75:
		tmp = t_1
	elif a <= 1.85e-135:
		tmp = t - (y * (x / -z))
	elif a <= 1.5e+92:
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / t)))
	tmp = 0.0
	if (a <= -5.6e+75)
		tmp = t_1;
	elseif (a <= 1.85e-135)
		tmp = Float64(t - Float64(y * Float64(x / Float64(-z))));
	elseif (a <= 1.5e+92)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / t));
	tmp = 0.0;
	if (a <= -5.6e+75)
		tmp = t_1;
	elseif (a <= 1.85e-135)
		tmp = t - (y * (x / -z));
	elseif (a <= 1.5e+92)
		tmp = y * ((t - x) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.6e+75], t$95$1, If[LessEqual[a, 1.85e-135], N[(t - N[(y * N[(x / (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e+92], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.60000000000000023e75 or 1.50000000000000007e92 < a

   1. Initial program 74.9%

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

      1. +-commutative 74.9%

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

      2. associate-*l/ 88.6%

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

      3. fma-def 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in z around 0 67.7%

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

      1. +-commutative 67.7%

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

      2. associate-/l* 74.5%

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

   6. Simplified 74.5%

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

   7. Taylor expanded in t around inf 69.5%

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

   if -5.60000000000000023e75 < a < 1.8499999999999999e-135

   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. associate-*l/ 69.8%

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

      3. fma-def 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in z around -inf 79.5%

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

   5. Taylor expanded in a around 0 76.2%

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

      1. mul-1-neg 76.2%

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

      2. unsub-neg 76.2%

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

      3. associate-/l* 77.8%

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

   7. Simplified 77.8%

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

   8. Taylor expanded in t around 0 61.3%

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

      1. associate-/l* 63.9%

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

      2. associate-*r/ 63.9%

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

      3. *-commutative 63.9%

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

      4. associate-*l/ 63.9%

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

      5. metadata-eval 63.9%

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

      6. times-frac 63.9%

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

      7. *-commutative 63.9%

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

      8. associate-*r/ 63.9%

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

      9. mul-1-neg 63.9%

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

      10. distribute-frac-neg 63.9%

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

      11. associate-/r/ 63.9%

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

      12. associate-*l/ 64.0%

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

      13. *-lft-identity 64.0%

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

   10. Simplified 64.0%

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

   if 1.8499999999999999e-135 < a < 1.50000000000000007e92

   1. Initial program 67.9%

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

      1. +-commutative 67.9%

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

      2. associate-*l/ 80.0%

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

      3. fma-def 80.0%

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

   3. Simplified 80.0%

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

   4. Taylor expanded in y around inf 66.6%

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

      1. div-sub 66.6%

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

      2. *-commutative 66.6%

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

   6. Simplified 66.6%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-135}:\\ \;\;\;\;t - y \cdot \frac{x}{-z}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+92}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 13: 54.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.36 \cdot 10^{-117}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 8000000000:\\ \;\;\;\;y \cdot \frac{-x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a t)))))
   (if (<= a -5.6e+75)
     t_1
     (if (<= a 1.36e-117)
       (- t (* t (/ y z)))
       (if (<= a 8000000000.0) (* y (/ (- x) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double tmp;
	if (a <= -5.6e+75) {
		tmp = t_1;
	} else if (a <= 1.36e-117) {
		tmp = t - (t * (y / z));
	} else if (a <= 8000000000.0) {
		tmp = y * (-x / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / t))
    if (a <= (-5.6d+75)) then
        tmp = t_1
    else if (a <= 1.36d-117) then
        tmp = t - (t * (y / z))
    else if (a <= 8000000000.0d0) then
        tmp = y * (-x / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double tmp;
	if (a <= -5.6e+75) {
		tmp = t_1;
	} else if (a <= 1.36e-117) {
		tmp = t - (t * (y / z));
	} else if (a <= 8000000000.0) {
		tmp = y * (-x / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / t))
	tmp = 0
	if a <= -5.6e+75:
		tmp = t_1
	elif a <= 1.36e-117:
		tmp = t - (t * (y / z))
	elif a <= 8000000000.0:
		tmp = y * (-x / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / t)))
	tmp = 0.0
	if (a <= -5.6e+75)
		tmp = t_1;
	elseif (a <= 1.36e-117)
		tmp = Float64(t - Float64(t * Float64(y / z)));
	elseif (a <= 8000000000.0)
		tmp = Float64(y * Float64(Float64(-x) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / t));
	tmp = 0.0;
	if (a <= -5.6e+75)
		tmp = t_1;
	elseif (a <= 1.36e-117)
		tmp = t - (t * (y / z));
	elseif (a <= 8000000000.0)
		tmp = y * (-x / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.6e+75], t$95$1, If[LessEqual[a, 1.36e-117], N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8000000000.0], N[(y * N[((-x) / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.60000000000000023e75 or 8e9 < a

   1. Initial program 75.1%

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

      1. +-commutative 75.1%

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

      2. associate-*l/ 88.5%

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

      3. fma-def 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in z around 0 68.0%

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

      1. +-commutative 68.0%

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

      2. associate-/l* 73.8%

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

   6. Simplified 73.8%

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

   7. Taylor expanded in t around inf 66.1%

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

   if -5.60000000000000023e75 < a < 1.35999999999999996e-117

   1. Initial program 63.7%

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

      1. +-commutative 63.7%

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

      2. associate-*l/ 70.8%

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

      3. fma-def 70.9%

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

   3. Simplified 70.9%

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

   4. Taylor expanded in z around -inf 77.8%

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

   5. Taylor expanded in a around 0 74.6%

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

      1. mul-1-neg 74.6%

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

      2. unsub-neg 74.6%

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

      3. associate-/l* 76.9%

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

   7. Simplified 76.9%

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

   8. Taylor expanded in t around inf 59.0%

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

      1. associate-*l/ 59.8%

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

      2. *-commutative 59.8%

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

   10. Simplified 59.8%

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

   if 1.35999999999999996e-117 < a < 8e9

   1. Initial program 61.3%

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

      1. +-commutative 61.3%

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

      2. associate-*l/ 71.8%

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

      3. fma-def 71.8%

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

   3. Simplified 71.8%

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

   4. Taylor expanded in y around -inf 52.7%

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

   5. Taylor expanded in t around 0 36.2%

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

      1. mul-1-neg 36.2%

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

      2. distribute-rgt-neg-in 36.2%

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

   7. Simplified 36.2%

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

   8. Taylor expanded in y around 0 36.2%

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

      1. mul-1-neg 36.2%

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

      2. associate-*r/ 50.8%

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

      3. distribute-rgt-neg-in 50.8%

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

   10. Simplified 50.8%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq 1.36 \cdot 10^{-117}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 8000000000:\\ \;\;\;\;y \cdot \frac{-x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 14: 59.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-28} \lor \neg \left(z \leq 7.1 \cdot 10^{+50}\right):\\ \;\;\;\;t - y \cdot \frac{x}{-z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6e-28) (not (<= z 7.1e+50)))
   (- t (* y (/ x (- z))))
   (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6e-28) || !(z <= 7.1e+50)) {
		tmp = t - (y * (x / -z));
	} else {
		tmp = x + (y / (a / 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 <= (-6d-28)) .or. (.not. (z <= 7.1d+50))) then
        tmp = t - (y * (x / -z))
    else
        tmp = x + (y / (a / 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 <= -6e-28) || !(z <= 7.1e+50)) {
		tmp = t - (y * (x / -z));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6e-28) or not (z <= 7.1e+50):
		tmp = t - (y * (x / -z))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6e-28) || !(z <= 7.1e+50))
		tmp = Float64(t - Float64(y * Float64(x / Float64(-z))));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6e-28) || ~((z <= 7.1e+50)))
		tmp = t - (y * (x / -z));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6e-28], N[Not[LessEqual[z, 7.1e+50]], $MachinePrecision]], N[(t - N[(y * N[(x / (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.00000000000000005e-28 or 7.09999999999999992e50 < z

   1. Initial program 44.3%

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

      1. +-commutative 44.3%

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

      2. associate-*l/ 65.4%

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

      3. fma-def 65.3%

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

   3. Simplified 65.3%

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

   4. Taylor expanded in z around -inf 61.0%

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

   5. Taylor expanded in a around 0 58.3%

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

      1. mul-1-neg 58.3%

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

      2. unsub-neg 58.3%

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

      3. associate-/l* 68.6%

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

   7. Simplified 68.6%

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

   8. Taylor expanded in t around 0 54.3%

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

      1. associate-/l* 61.7%

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

      2. associate-*r/ 61.7%

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

      3. *-commutative 61.7%

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

      4. associate-*l/ 61.7%

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

      5. metadata-eval 61.7%

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

      6. times-frac 61.7%

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

      7. *-commutative 61.7%

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

      8. associate-*r/ 61.7%

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

      9. mul-1-neg 61.7%

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

      10. distribute-frac-neg 61.7%

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

      11. associate-/r/ 61.7%

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

      12. associate-*l/ 61.8%

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

      13. *-lft-identity 61.8%

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

   10. Simplified 61.8%

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

   if -6.00000000000000005e-28 < z < 7.09999999999999992e50

   1. Initial program 92.7%

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

      1. +-commutative 92.7%

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

      2. associate-*l/ 92.1%

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

      3. fma-def 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in z around 0 72.1%

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

      1. +-commutative 72.1%

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

      2. associate-/l* 72.7%

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

   6. Simplified 72.7%

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

   7. Taylor expanded in t around inf 61.6%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-28} \lor \neg \left(z \leq 7.1 \cdot 10^{+50}\right):\\ \;\;\;\;t - y \cdot \frac{x}{-z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 15: 37.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-116}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 36000000000000:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.6e+75)
   x
   (if (<= a 2.5e-116) t (if (<= a 36000000000000.0) (* y (/ x z)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.6e+75) {
		tmp = x;
	} else if (a <= 2.5e-116) {
		tmp = t;
	} else if (a <= 36000000000000.0) {
		tmp = y * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.6d+75)) then
        tmp = x
    else if (a <= 2.5d-116) then
        tmp = t
    else if (a <= 36000000000000.0d0) then
        tmp = y * (x / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.6e+75) {
		tmp = x;
	} else if (a <= 2.5e-116) {
		tmp = t;
	} else if (a <= 36000000000000.0) {
		tmp = y * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.6e+75:
		tmp = x
	elif a <= 2.5e-116:
		tmp = t
	elif a <= 36000000000000.0:
		tmp = y * (x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.6e+75)
		tmp = x;
	elseif (a <= 2.5e-116)
		tmp = t;
	elseif (a <= 36000000000000.0)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.6e+75)
		tmp = x;
	elseif (a <= 2.5e-116)
		tmp = t;
	elseif (a <= 36000000000000.0)
		tmp = y * (x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.6e+75], x, If[LessEqual[a, 2.5e-116], t, If[LessEqual[a, 36000000000000.0], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.59999999999999996e75 or 3.6e13 < a

   1. Initial program 75.1%

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

      1. +-commutative 75.1%

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

      2. associate-*l/ 88.5%

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

      3. fma-def 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in a around inf 49.2%

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

   if -6.59999999999999996e75 < a < 2.5000000000000001e-116

   1. Initial program 63.7%

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

      1. +-commutative 63.7%

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

      2. associate-*l/ 70.8%

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

      3. fma-def 70.9%

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

   3. Simplified 70.9%

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

   4. Taylor expanded in z around inf 42.2%

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

   if 2.5000000000000001e-116 < a < 3.6e13

   1. Initial program 61.3%

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

      1. +-commutative 61.3%

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

      2. associate-*l/ 71.8%

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

      3. fma-def 71.8%

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

   3. Simplified 71.8%

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

   4. Taylor expanded in y around -inf 52.7%

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

   5. Taylor expanded in t around 0 36.2%

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

      1. mul-1-neg 36.2%

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

      2. distribute-rgt-neg-in 36.2%

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

   7. Simplified 36.2%

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

   8. Taylor expanded in a around 0 35.7%

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

      1. associate-/l* 50.2%

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

   10. Simplified 50.2%

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

   11. Taylor expanded in y around 0 35.7%

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

       1. associate-*r/ 50.1%

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

   13. Simplified 50.1%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-116}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 36000000000000:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 53.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+84}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+50}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.3e+84) t (if (<= z 8e+50) (+ x (* t (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+84) {
		tmp = t;
	} else if (z <= 8e+50) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.3d+84)) then
        tmp = t
    else if (z <= 8d+50) then
        tmp = x + (t * (y / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+84) {
		tmp = t;
	} else if (z <= 8e+50) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.3e+84:
		tmp = t
	elif z <= 8e+50:
		tmp = x + (t * (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.3e+84)
		tmp = t;
	elseif (z <= 8e+50)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.3e+84)
		tmp = t;
	elseif (z <= 8e+50)
		tmp = x + (t * (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.3e+84], t, If[LessEqual[z, 8e+50], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3000000000000001e84 or 8.0000000000000006e50 < z

   1. Initial program 37.4%

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

      1. +-commutative 37.4%

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

      2. associate-*l/ 60.8%

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

      3. fma-def 60.8%

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

   3. Simplified 60.8%

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

   4. Taylor expanded in z around inf 45.3%

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

   if -1.3000000000000001e84 < z < 8.0000000000000006e50

   1. Initial program 90.5%

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

      1. +-commutative 90.5%

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

      2. associate-*l/ 91.4%

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

      3. fma-def 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in z around 0 67.0%

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

      1. +-commutative 67.0%

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

      2. associate-/l* 68.9%

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

   6. Simplified 68.9%

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

   7. Taylor expanded in t around inf 56.3%

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

      1. associate-*l/ 55.8%

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

      2. *-commutative 55.8%

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

   9. Simplified 55.8%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+84}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+50}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 17: 52.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+83}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+51}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.5e+83) t (if (<= z 3.3e+51) (+ x (/ y (/ a t))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+83) {
		tmp = t;
	} else if (z <= 3.3e+51) {
		tmp = x + (y / (a / t));
	} 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 <= (-4.5d+83)) then
        tmp = t
    else if (z <= 3.3d+51) then
        tmp = x + (y / (a / t))
    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 <= -4.5e+83) {
		tmp = t;
	} else if (z <= 3.3e+51) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.5e+83:
		tmp = t
	elif z <= 3.3e+51:
		tmp = x + (y / (a / t))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.5e+83)
		tmp = t;
	elseif (z <= 3.3e+51)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.5e+83)
		tmp = t;
	elseif (z <= 3.3e+51)
		tmp = x + (y / (a / t));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.5e+83], t, If[LessEqual[z, 3.3e+51], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4999999999999999e83 or 3.2999999999999997e51 < z

   1. Initial program 37.4%

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

      1. +-commutative 37.4%

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

      2. associate-*l/ 60.8%

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

      3. fma-def 60.8%

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

   3. Simplified 60.8%

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

   4. Taylor expanded in z around inf 45.3%

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

   if -4.4999999999999999e83 < z < 3.2999999999999997e51

   1. Initial program 90.5%

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

      1. +-commutative 90.5%

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

      2. associate-*l/ 91.4%

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

      3. fma-def 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in z around 0 67.0%

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

      1. +-commutative 67.0%

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

      2. associate-/l* 68.9%

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

   6. Simplified 68.9%

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

   7. Taylor expanded in t around inf 56.9%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+83}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+51}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18: 38.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+27}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6e+75) x (if (<= a 7.8e+27) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6e+75) {
		tmp = x;
	} else if (a <= 7.8e+27) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6d+75)) then
        tmp = x
    else if (a <= 7.8d+27) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6e+75) {
		tmp = x;
	} else if (a <= 7.8e+27) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6e+75:
		tmp = x
	elif a <= 7.8e+27:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6e+75)
		tmp = x;
	elseif (a <= 7.8e+27)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6e+75)
		tmp = x;
	elseif (a <= 7.8e+27)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6e+75], x, If[LessEqual[a, 7.8e+27], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -6e75 or 7.7999999999999997e27 < a

   1. Initial program 75.0%

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

      1. +-commutative 75.0%

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

      2. associate-*l/ 89.0%

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

      3. fma-def 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in a around inf 50.0%

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

   if -6e75 < a < 7.7999999999999997e27

   1. Initial program 63.6%

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

      1. +-commutative 63.6%

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

      2. associate-*l/ 71.1%

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

      3. fma-def 71.2%

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

   3. Simplified 71.2%

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

   4. Taylor expanded in z around inf 37.8%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+27}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 2.8% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.5%

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

   1. +-commutative 68.5%

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

   2. associate-*l/ 78.7%

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

   3. fma-def 78.7%

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

3. Simplified 78.7%

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

4. Taylor expanded in y around 0 39.4%

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

   1. +-commutative 39.4%

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

   2. *-commutative 39.4%

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

   3. mul-1-neg 39.4%

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

   4. associate-*r/ 43.1%

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

   5. unsub-neg 43.1%

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

6. Simplified 43.1%

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

7. Taylor expanded in x around inf 26.5%

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

   1. *-commutative 26.5%

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

   2. sub-neg 26.5%

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

   3. mul-1-neg 26.5%

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

   4. remove-double-neg 26.5%

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

   5. distribute-lft-in 26.6%

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

   6. *-rgt-identity 26.6%

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

9. Simplified 26.6%

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

10. Taylor expanded in z around inf 2.9%

    \[\leadsto \color{blue}{-1 \cdot x + x} \]
11. Step-by-step derivation

    1. distribute-lft1-in 2.9%

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

    2. metadata-eval 2.9%

       \[\leadsto \color{blue}{0} \cdot x \]

    3. mul0-lft 2.9%

       \[\leadsto \color{blue}{0} \]

12. Simplified 2.9%

    \[\leadsto \color{blue}{0} \]

13. Final simplification 2.9%

    \[\leadsto 0 \]

Alternative 20: 25.4% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.5%

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

   1. +-commutative 68.5%

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

   2. associate-*l/ 78.7%

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

   3. fma-def 78.7%

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

3. Simplified 78.7%

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

4. Taylor expanded in z around inf 26.3%

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

5. Final simplification 26.3%

   \[\leadsto t \]

Developer target: 83.8% accurate, 0.8× 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 2023257 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

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