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

Percentage Accurate: 68.1% → 91.1%

Time: 17.5s

Alternatives: 23

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-294}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+284}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z)))))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -1e-294)
       t_2
       (if (<= t_2 0.0)
         (- t (/ (* (- t x) (- y a)) z))
         (if (<= t_2 2e+284) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -1e-294) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t - (((t - x) * (y - a)) / z);
	} else if (t_2 <= 2e+284) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	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 t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -1e-294) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t - (((t - x) * (y - a)) / z);
	} else if (t_2 <= 2e+284) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	t_2 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -1e-294:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t - (((t - x) * (y - a)) / z)
	elif t_2 <= 2e+284:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -1e-294)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t - Float64(Float64(Float64(t - x) * Float64(y - a)) / z));
	elseif (t_2 <= 2e+284)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	t_2 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -1e-294)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t - (((t - x) * (y - a)) / z);
	elseif (t_2 <= 2e+284)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -1e-294], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t - N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+284], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -inf.0 or 2.00000000000000016e284 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 33.8%

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

      1. associate-/l* 79.2%

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

   3. Simplified 79.2%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.00000000000000002e-294 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 2.00000000000000016e284

   1. Initial program 94.7%

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

   if -1.00000000000000002e-294 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.3%

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

      1. +-commutative 4.3%

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

      2. *-commutative 4.3%

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

      3. associate-/l* 4.3%

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

      4. fma-define 4.3%

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

   3. Simplified 4.3%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. div-sub 99.9%

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

      6. mul-1-neg 99.9%

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

      7. distribute-lft-out-- 99.9%

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

      8. associate-*r/ 99.9%

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

      9. mul-1-neg 99.9%

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

      10. unsub-neg 99.9%

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

      11. distribute-rgt-out-- 99.9%

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

   7. Simplified 99.9%

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

Alternative 2: 90.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-294} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -1e-294) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (- t (/ (* (- t x) (- y a)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-294) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = t - (((t - x) * (y - a)) / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -1e-294) || !(t_1 <= 0.0))
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(t - Float64(Float64(Float64(t - x) * Float64(y - a)) / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-294], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(t - N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.00000000000000002e-294 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 70.0%

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

      1. +-commutative 70.0%

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

      2. *-commutative 70.0%

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

      3. associate-/l* 87.6%

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

      4. fma-define 87.7%

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

   3. Simplified 87.7%

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

   if -1.00000000000000002e-294 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.3%

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

      1. +-commutative 4.3%

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

      2. *-commutative 4.3%

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

      3. associate-/l* 4.3%

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

      4. fma-define 4.3%

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

   3. Simplified 4.3%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. div-sub 99.9%

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

      6. mul-1-neg 99.9%

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

      7. distribute-lft-out-- 99.9%

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

      8. associate-*r/ 99.9%

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

      9. mul-1-neg 99.9%

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

      10. unsub-neg 99.9%

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

      11. distribute-rgt-out-- 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-294} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-294} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -1e-294) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (- t (/ (* (- t x) (- y a)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-294) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t - (((t - x) * (y - 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) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) * (t - x)) / (a - z))
    if ((t_1 <= (-1d-294)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t - (((t - x) * (y - a)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-294) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t - (((t - x) * (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 <= -1e-294) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t - (((t - x) * (y - a)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -1e-294) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t - Float64(Float64(Float64(t - x) * Float64(y - 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 <= -1e-294) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t - (((t - x) * (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, -1e-294], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.00000000000000002e-294 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 70.0%

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

      1. associate-/l* 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in y around 0 70.1%

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

      1. mul-1-neg 70.1%

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

      2. associate-/l* 80.4%

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

      3. distribute-lft-neg-out 80.4%

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

      4. +-commutative 80.4%

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

      5. div-sub 80.8%

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

      6. distribute-rgt-out 82.5%

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

      7. sub-neg 82.5%

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

      8. associate-/r/ 87.6%

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

   7. Simplified 87.6%

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

   if -1.00000000000000002e-294 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.3%

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

      1. +-commutative 4.3%

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

      2. *-commutative 4.3%

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

      3. associate-/l* 4.3%

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

      4. fma-define 4.3%

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

   3. Simplified 4.3%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. div-sub 99.9%

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

      6. mul-1-neg 99.9%

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

      7. distribute-lft-out-- 99.9%

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

      8. associate-*r/ 99.9%

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

      9. mul-1-neg 99.9%

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

      10. unsub-neg 99.9%

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

      11. distribute-rgt-out-- 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-294} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+245}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.75:\\ \;\;\;\;x - t \cdot \frac{z - y}{a - z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-147}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+230}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a (/ x z)))))
   (if (<= z -2e+245)
     t_1
     (if (<= z -1.75)
       (- x (* t (/ (- z y) (- a z))))
       (if (<= z 6.5e-147)
         (+ x (/ (- t x) (/ (- a z) y)))
         (if (<= z 6.8e+230) (+ x (* (- y z) (/ t (- a z)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * (x / z));
	double tmp;
	if (z <= -2e+245) {
		tmp = t_1;
	} else if (z <= -1.75) {
		tmp = x - (t * ((z - y) / (a - z)));
	} else if (z <= 6.5e-147) {
		tmp = x + ((t - x) / ((a - z) / y));
	} else if (z <= 6.8e+230) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - (a * (x / z))
    if (z <= (-2d+245)) then
        tmp = t_1
    else if (z <= (-1.75d0)) then
        tmp = x - (t * ((z - y) / (a - z)))
    else if (z <= 6.5d-147) then
        tmp = x + ((t - x) / ((a - z) / y))
    else if (z <= 6.8d+230) then
        tmp = x + ((y - z) * (t / (a - z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * (x / z));
	double tmp;
	if (z <= -2e+245) {
		tmp = t_1;
	} else if (z <= -1.75) {
		tmp = x - (t * ((z - y) / (a - z)));
	} else if (z <= 6.5e-147) {
		tmp = x + ((t - x) / ((a - z) / y));
	} else if (z <= 6.8e+230) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a * (x / z))
	tmp = 0
	if z <= -2e+245:
		tmp = t_1
	elif z <= -1.75:
		tmp = x - (t * ((z - y) / (a - z)))
	elif z <= 6.5e-147:
		tmp = x + ((t - x) / ((a - z) / y))
	elif z <= 6.8e+230:
		tmp = x + ((y - z) * (t / (a - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a * Float64(x / z)))
	tmp = 0.0
	if (z <= -2e+245)
		tmp = t_1;
	elseif (z <= -1.75)
		tmp = Float64(x - Float64(t * Float64(Float64(z - y) / Float64(a - z))));
	elseif (z <= 6.5e-147)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / y)));
	elseif (z <= 6.8e+230)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a * (x / z));
	tmp = 0.0;
	if (z <= -2e+245)
		tmp = t_1;
	elseif (z <= -1.75)
		tmp = x - (t * ((z - y) / (a - z)));
	elseif (z <= 6.5e-147)
		tmp = x + ((t - x) / ((a - z) / y));
	elseif (z <= 6.8e+230)
		tmp = x + ((y - z) * (t / (a - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+245], t$95$1, If[LessEqual[z, -1.75], N[(x - N[(t * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e-147], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+230], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.00000000000000009e245 or 6.79999999999999973e230 < z

   1. Initial program 29.5%

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

      1. associate-/l* 27.4%

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

   3. Simplified 27.4%

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

   5. Taylor expanded in y around 0 28.4%

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

      1. mul-1-neg 28.4%

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

      2. associate-/l* 27.4%

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

      3. distribute-lft-neg-out 27.4%

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

      4. *-commutative 27.4%

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

   7. Simplified 27.4%

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

   8. Taylor expanded in z around inf 78.2%

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

      1. associate-/l* 89.6%

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

   10. Simplified 89.6%

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

   11. Taylor expanded in t around 0 89.6%

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

       1. neg-mul-1 89.6%

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

   13. Simplified 89.6%

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

       1. *-commutative 89.6%

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

       2. add-sqr-sqrt 57.1%

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

       3. sqrt-unprod 69.3%

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

       4. sqr-neg 69.3%

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

       5. sqrt-unprod 29.4%

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

       6. add-sqr-sqrt 69.2%

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

       7. cancel-sign-sub 69.2%

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

       8. distribute-frac-neg 69.2%

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

       9. *-commutative 69.2%

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

       10. add-sqr-sqrt 39.7%

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

       11. sqrt-unprod 60.4%

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

       12. sqr-neg 60.4%

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

       13. sqrt-unprod 32.4%

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

       14. add-sqr-sqrt 89.6%

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

   15. Applied egg-rr 89.6%

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

   if -2.00000000000000009e245 < z < -1.75

   1. Initial program 50.1%

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

      1. associate-/l* 71.7%

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

   3. Simplified 71.7%

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

   5. Taylor expanded in t around inf 48.3%

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

      1. associate-/l* 67.1%

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

   7. Simplified 67.1%

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

   if -1.75 < z < 6.49999999999999967e-147

   1. Initial program 87.5%

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

      1. associate-/l* 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in y around 0 89.6%

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

      1. mul-1-neg 89.6%

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

      2. associate-/l* 84.8%

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

      3. distribute-lft-neg-out 84.8%

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

      4. +-commutative 84.8%

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

      5. div-sub 86.0%

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

      6. distribute-rgt-out 90.8%

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

      7. sub-neg 90.8%

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

      8. associate-/r/ 94.0%

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

   7. Simplified 94.0%

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

   8. Taylor expanded in y around inf 87.8%

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

   if 6.49999999999999967e-147 < z < 6.79999999999999973e230

   1. Initial program 68.1%

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

      1. associate-/l* 85.5%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in t around inf 68.7%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+245}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.75:\\ \;\;\;\;x - t \cdot \frac{z - y}{a - z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-147}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+230}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot \frac{z - y}{a - z}\\ t_2 := t - a \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+252}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -75:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-47}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+231}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* t (/ (- z y) (- a z))))) (t_2 (- t (* a (/ x z)))))
   (if (<= z -2e+252)
     t_2
     (if (<= z -75.0)
       t_1
       (if (<= z 9.5e-47)
         (+ x (* y (/ (- t x) (- a z))))
         (if (<= z 4.5e+231) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * ((z - y) / (a - z)));
	double t_2 = t - (a * (x / z));
	double tmp;
	if (z <= -2e+252) {
		tmp = t_2;
	} else if (z <= -75.0) {
		tmp = t_1;
	} else if (z <= 9.5e-47) {
		tmp = x + (y * ((t - x) / (a - z)));
	} else if (z <= 4.5e+231) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (t * ((z - y) / (a - z)))
    t_2 = t - (a * (x / z))
    if (z <= (-2d+252)) then
        tmp = t_2
    else if (z <= (-75.0d0)) then
        tmp = t_1
    else if (z <= 9.5d-47) then
        tmp = x + (y * ((t - x) / (a - z)))
    else if (z <= 4.5d+231) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * ((z - y) / (a - z)));
	double t_2 = t - (a * (x / z));
	double tmp;
	if (z <= -2e+252) {
		tmp = t_2;
	} else if (z <= -75.0) {
		tmp = t_1;
	} else if (z <= 9.5e-47) {
		tmp = x + (y * ((t - x) / (a - z)));
	} else if (z <= 4.5e+231) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t * ((z - y) / (a - z)))
	t_2 = t - (a * (x / z))
	tmp = 0
	if z <= -2e+252:
		tmp = t_2
	elif z <= -75.0:
		tmp = t_1
	elif z <= 9.5e-47:
		tmp = x + (y * ((t - x) / (a - z)))
	elif z <= 4.5e+231:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t * Float64(Float64(z - y) / Float64(a - z))))
	t_2 = Float64(t - Float64(a * Float64(x / z)))
	tmp = 0.0
	if (z <= -2e+252)
		tmp = t_2;
	elseif (z <= -75.0)
		tmp = t_1;
	elseif (z <= 9.5e-47)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / Float64(a - z))));
	elseif (z <= 4.5e+231)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t * ((z - y) / (a - z)));
	t_2 = t - (a * (x / z));
	tmp = 0.0;
	if (z <= -2e+252)
		tmp = t_2;
	elseif (z <= -75.0)
		tmp = t_1;
	elseif (z <= 9.5e-47)
		tmp = x + (y * ((t - x) / (a - z)));
	elseif (z <= 4.5e+231)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(t * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(a * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+252], t$95$2, If[LessEqual[z, -75.0], t$95$1, If[LessEqual[z, 9.5e-47], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+231], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0000000000000002e252 or 4.49999999999999991e231 < z

   1. Initial program 29.5%

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

      1. associate-/l* 27.4%

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

   3. Simplified 27.4%

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

   5. Taylor expanded in y around 0 28.4%

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

      1. mul-1-neg 28.4%

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

      2. associate-/l* 27.4%

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

      3. distribute-lft-neg-out 27.4%

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

      4. *-commutative 27.4%

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

   7. Simplified 27.4%

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

   8. Taylor expanded in z around inf 78.2%

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

      1. associate-/l* 89.6%

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

   10. Simplified 89.6%

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

   11. Taylor expanded in t around 0 89.6%

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

       1. neg-mul-1 89.6%

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

   13. Simplified 89.6%

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

       1. *-commutative 89.6%

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

       2. add-sqr-sqrt 57.1%

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

       3. sqrt-unprod 69.3%

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

       4. sqr-neg 69.3%

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

       5. sqrt-unprod 29.4%

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

       6. add-sqr-sqrt 69.2%

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

       7. cancel-sign-sub 69.2%

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

       8. distribute-frac-neg 69.2%

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

       9. *-commutative 69.2%

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

       10. add-sqr-sqrt 39.7%

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

       11. sqrt-unprod 60.4%

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

       12. sqr-neg 60.4%

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

       13. sqrt-unprod 32.4%

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

       14. add-sqr-sqrt 89.6%

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

   15. Applied egg-rr 89.6%

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

   if -2.0000000000000002e252 < z < -75 or 9.4999999999999991e-47 < z < 4.49999999999999991e231

   1. Initial program 53.7%

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

      1. associate-/l* 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in t around inf 47.9%

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

      1. associate-/l* 66.0%

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

   7. Simplified 66.0%

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

   if -75 < z < 9.4999999999999991e-47

   1. Initial program 89.3%

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

      1. associate-/l* 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in y around inf 82.5%

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

      1. associate-*r/ 85.3%

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

   7. Simplified 85.3%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+252}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -75:\\ \;\;\;\;x - t \cdot \frac{z - y}{a - z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-47}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+231}:\\ \;\;\;\;x - t \cdot \frac{z - y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot \frac{z - y}{a - z}\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{-107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-182}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-26}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* t (/ (- z y) (- a z))))))
   (if (<= a -1.05e-107)
     t_1
     (if (<= a -5.2e-182)
       (+ t (* a (/ (- t x) z)))
       (if (<= a 3.3e-26) (* t (/ (- y z) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * ((z - y) / (a - z)));
	double tmp;
	if (a <= -1.05e-107) {
		tmp = t_1;
	} else if (a <= -5.2e-182) {
		tmp = t + (a * ((t - x) / z));
	} else if (a <= 3.3e-26) {
		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 - (t * ((z - y) / (a - z)))
    if (a <= (-1.05d-107)) then
        tmp = t_1
    else if (a <= (-5.2d-182)) then
        tmp = t + (a * ((t - x) / z))
    else if (a <= 3.3d-26) 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 - (t * ((z - y) / (a - z)));
	double tmp;
	if (a <= -1.05e-107) {
		tmp = t_1;
	} else if (a <= -5.2e-182) {
		tmp = t + (a * ((t - x) / z));
	} else if (a <= 3.3e-26) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t * ((z - y) / (a - z)))
	tmp = 0
	if a <= -1.05e-107:
		tmp = t_1
	elif a <= -5.2e-182:
		tmp = t + (a * ((t - x) / z))
	elif a <= 3.3e-26:
		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(t * Float64(Float64(z - y) / Float64(a - z))))
	tmp = 0.0
	if (a <= -1.05e-107)
		tmp = t_1;
	elseif (a <= -5.2e-182)
		tmp = Float64(t + Float64(a * Float64(Float64(t - x) / z)));
	elseif (a <= 3.3e-26)
		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 - (t * ((z - y) / (a - z)));
	tmp = 0.0;
	if (a <= -1.05e-107)
		tmp = t_1;
	elseif (a <= -5.2e-182)
		tmp = t + (a * ((t - x) / z));
	elseif (a <= 3.3e-26)
		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[(t * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.05e-107], t$95$1, If[LessEqual[a, -5.2e-182], N[(t + N[(a * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e-26], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.05e-107 or 3.2999999999999998e-26 < a

   1. Initial program 67.6%

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

      1. associate-/l* 84.6%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in t around inf 61.7%

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

      1. associate-/l* 76.0%

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

   7. Simplified 76.0%

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

   if -1.05e-107 < a < -5.20000000000000011e-182

   1. Initial program 33.3%

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

      1. associate-/l* 47.5%

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

   3. Simplified 47.5%

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

   5. Taylor expanded in y around 0 8.6%

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

      1. mul-1-neg 8.6%

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

      2. associate-/l* 22.8%

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

      3. distribute-lft-neg-out 22.8%

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

      4. *-commutative 22.8%

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

   7. Simplified 22.8%

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

   8. Taylor expanded in z around inf 65.4%

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

      1. associate-/l* 69.7%

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

   10. Simplified 69.7%

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

   if -5.20000000000000011e-182 < a < 3.2999999999999998e-26

   1. Initial program 66.6%

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

      1. +-commutative 66.6%

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

      2. *-commutative 66.6%

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

      3. associate-/l* 73.7%

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

      4. fma-define 73.7%

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

   3. Simplified 73.7%

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

   5. Taylor expanded in t around inf 75.1%

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

   6. Taylor expanded in x around 0 71.7%

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

      1. div-sub 71.7%

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

   8. Simplified 71.7%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-107}:\\ \;\;\;\;x - t \cdot \frac{z - y}{a - z}\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-182}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-26}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{z - y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+229}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 1.76 \cdot 10^{+230}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e+229)
   (+ t (/ a (/ z (- t x))))
   (if (<= z 1.76e+230)
     (+ x (* (- y z) (/ (- t x) (- a z))))
     (- t (* a (/ x z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+229) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= 1.76e+230) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = t - (a * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2d+229)) then
        tmp = t + (a / (z / (t - x)))
    else if (z <= 1.76d+230) then
        tmp = x + ((y - z) * ((t - x) / (a - z)))
    else
        tmp = t - (a * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+229) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= 1.76e+230) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = t - (a * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e+229:
		tmp = t + (a / (z / (t - x)))
	elif z <= 1.76e+230:
		tmp = x + ((y - z) * ((t - x) / (a - z)))
	else:
		tmp = t - (a * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e+229)
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	elseif (z <= 1.76e+230)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))));
	else
		tmp = Float64(t - Float64(a * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2e+229)
		tmp = t + (a / (z / (t - x)));
	elseif (z <= 1.76e+230)
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	else
		tmp = t - (a * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e+229], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.76e+230], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(a * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2e229

   1. Initial program 44.0%

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

      1. associate-/l* 29.2%

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

   3. Simplified 29.2%

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

   5. Taylor expanded in y around 0 37.8%

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

      1. mul-1-neg 37.8%

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

      2. associate-/l* 29.2%

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

      3. distribute-lft-neg-out 29.2%

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

      4. *-commutative 29.2%

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

   7. Simplified 29.2%

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

   8. Taylor expanded in z around inf 65.9%

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

      1. associate-/l* 83.7%

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

   10. Simplified 83.7%

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

       1. clear-num 83.6%

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

       2. un-div-inv 83.8%

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

   12. Applied egg-rr 83.8%

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

   if -2e229 < z < 1.76000000000000003e230

   1. Initial program 69.7%

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

      1. associate-/l* 83.9%

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

   3. Simplified 83.9%

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

   if 1.76000000000000003e230 < z

   1. Initial program 20.9%

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

      1. associate-/l* 29.6%

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

   3. Simplified 29.6%

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

   5. Taylor expanded in y around 0 20.9%

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

      1. mul-1-neg 20.9%

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

      2. associate-/l* 29.6%

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

      3. distribute-lft-neg-out 29.6%

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

      4. *-commutative 29.6%

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

   7. Simplified 29.6%

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

   8. Taylor expanded in z around inf 88.5%

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

      1. associate-/l* 94.2%

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

   10. Simplified 94.2%

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

   11. Taylor expanded in t around 0 94.2%

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

       1. neg-mul-1 94.2%

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

   13. Simplified 94.2%

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

       1. *-commutative 94.2%

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

       2. add-sqr-sqrt 52.9%

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

       3. sqrt-unprod 71.1%

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

       4. sqr-neg 71.1%

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

       5. sqrt-unprod 35.4%

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

       6. add-sqr-sqrt 76.9%

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

       7. cancel-sign-sub 76.9%

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

       8. distribute-frac-neg 76.9%

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

       9. *-commutative 76.9%

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

       10. add-sqr-sqrt 41.5%

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

       11. sqrt-unprod 65.6%

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

       12. sqr-neg 65.6%

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

       13. sqrt-unprod 41.2%

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

       14. add-sqr-sqrt 94.2%

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

   15. Applied egg-rr 94.2%

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

Alternative 8: 45.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+156}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-159}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.4e+156)
   t
   (if (<= z 2.4e-159)
     (* x (- 1.0 (/ y a)))
     (if (<= z 1.15e-17) (* t (/ y (- a z))) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e+156) {
		tmp = t;
	} else if (z <= 2.4e-159) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.15e-17) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.4d+156)) then
        tmp = t
    else if (z <= 2.4d-159) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.15d-17) then
        tmp = t * (y / (a - z))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e+156) {
		tmp = t;
	} else if (z <= 2.4e-159) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.15e-17) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.4e+156:
		tmp = t
	elif z <= 2.4e-159:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.15e-17:
		tmp = t * (y / (a - z))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.4e+156)
		tmp = t;
	elseif (z <= 2.4e-159)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.15e-17)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.4e+156)
		tmp = t;
	elseif (z <= 2.4e-159)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.15e-17)
		tmp = t * (y / (a - z));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.4e+156], t, If[LessEqual[z, 2.4e-159], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e-17], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4000000000000001e156 or 1.15000000000000004e-17 < z

   1. Initial program 41.9%

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

      1. associate-/l* 61.4%

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

   3. Simplified 61.4%

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

   5. Taylor expanded in y around 0 32.4%

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

      1. mul-1-neg 32.4%

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

      2. associate-/l* 46.3%

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

      3. distribute-lft-neg-out 46.3%

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

      4. *-commutative 46.3%

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

   7. Simplified 46.3%

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

   8. Taylor expanded in z around inf 53.0%

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

      1. associate-/l* 61.4%

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

   10. Simplified 61.4%

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

   11. Taylor expanded in t around 0 61.7%

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

       1. neg-mul-1 61.7%

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

   13. Simplified 61.7%

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

   14. Taylor expanded in t around inf 52.0%

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

   if -5.4000000000000001e156 < z < 2.39999999999999997e-159

   1. Initial program 77.8%

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

      1. associate-/l* 84.3%

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

   3. Simplified 84.3%

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

   5. Taylor expanded in z around 0 53.8%

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

   6. Taylor expanded in x around inf 43.2%

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

      1. mul-1-neg 43.2%

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

      2. unsub-neg 43.2%

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

   8. Simplified 43.2%

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

   if 2.39999999999999997e-159 < z < 1.15000000000000004e-17

   1. Initial program 87.4%

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

      1. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in t around inf 74.1%

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

      1. associate-/l* 74.1%

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

   7. Simplified 74.1%

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

   8. Taylor expanded in y around inf 61.5%

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

   9. Taylor expanded in x around 0 49.6%

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

       1. associate-/l* 49.7%

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

   11. Simplified 49.7%

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

Alternative 9: 75.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{-96} \lor \neg \left(a \leq 1.85 \cdot 10^{-12}\right):\\ \;\;\;\;x - t \cdot \frac{z - y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.7e-96) (not (<= a 1.85e-12)))
   (- x (* t (/ (- z y) (- a z))))
   (- t (/ (* (- t x) (- y a)) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.7e-96) || !(a <= 1.85e-12)) {
		tmp = x - (t * ((z - y) / (a - z)));
	} else {
		tmp = t - (((t - x) * (y - 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 ((a <= (-4.7d-96)) .or. (.not. (a <= 1.85d-12))) then
        tmp = x - (t * ((z - y) / (a - z)))
    else
        tmp = t - (((t - x) * (y - 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 ((a <= -4.7e-96) || !(a <= 1.85e-12)) {
		tmp = x - (t * ((z - y) / (a - z)));
	} else {
		tmp = t - (((t - x) * (y - a)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.7e-96) or not (a <= 1.85e-12):
		tmp = x - (t * ((z - y) / (a - z)))
	else:
		tmp = t - (((t - x) * (y - a)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.7e-96) || !(a <= 1.85e-12))
		tmp = Float64(x - Float64(t * Float64(Float64(z - y) / Float64(a - z))));
	else
		tmp = Float64(t - Float64(Float64(Float64(t - x) * Float64(y - a)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.7e-96) || ~((a <= 1.85e-12)))
		tmp = x - (t * ((z - y) / (a - z)));
	else
		tmp = t - (((t - x) * (y - a)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.7e-96], N[Not[LessEqual[a, 1.85e-12]], $MachinePrecision]], N[(x - N[(t * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.6999999999999998e-96 or 1.84999999999999999e-12 < a

   1. Initial program 67.2%

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

      1. associate-/l* 85.1%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in t around inf 61.4%

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

      1. associate-/l* 77.2%

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

   7. Simplified 77.2%

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

   if -4.6999999999999998e-96 < a < 1.84999999999999999e-12

   1. Initial program 60.7%

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

      1. +-commutative 60.7%

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

      2. *-commutative 60.7%

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

      3. associate-/l* 69.5%

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

      4. fma-define 69.6%

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

   3. Simplified 69.6%

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

   5. Taylor expanded in z around inf 83.7%

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

      1. associate--l+ 83.7%

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

      2. associate-*r/ 83.7%

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

      3. associate-*r/ 83.7%

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

      4. mul-1-neg 83.7%

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

      5. div-sub 83.7%

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

      6. mul-1-neg 83.7%

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

      7. distribute-lft-out-- 83.7%

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

      8. associate-*r/ 83.7%

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

      9. mul-1-neg 83.7%

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

      10. unsub-neg 83.7%

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

      11. distribute-rgt-out-- 83.7%

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

   7. Simplified 83.7%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{-96} \lor \neg \left(a \leq 1.85 \cdot 10^{-12}\right):\\ \;\;\;\;x - t \cdot \frac{z - y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+99}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-307}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 14500:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.5e+99)
   t
   (if (<= z 3.1e-307) x (if (<= z 14500.0) (* t (/ y a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e+99) {
		tmp = t;
	} else if (z <= 3.1e-307) {
		tmp = x;
	} else if (z <= 14500.0) {
		tmp = 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 <= (-3.5d+99)) then
        tmp = t
    else if (z <= 3.1d-307) then
        tmp = x
    else if (z <= 14500.0d0) then
        tmp = 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 <= -3.5e+99) {
		tmp = t;
	} else if (z <= 3.1e-307) {
		tmp = x;
	} else if (z <= 14500.0) {
		tmp = t * (y / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.5e+99:
		tmp = t
	elif z <= 3.1e-307:
		tmp = x
	elif z <= 14500.0:
		tmp = t * (y / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.5e+99)
		tmp = t;
	elseif (z <= 3.1e-307)
		tmp = x;
	elseif (z <= 14500.0)
		tmp = 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 <= -3.5e+99)
		tmp = t;
	elseif (z <= 3.1e-307)
		tmp = x;
	elseif (z <= 14500.0)
		tmp = t * (y / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.5e+99], t, If[LessEqual[z, 3.1e-307], x, If[LessEqual[z, 14500.0], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4999999999999998e99 or 14500 < 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. associate-/l* 61.1%

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

   3. Simplified 61.1%

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

   5. Taylor expanded in y around 0 30.9%

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

      1. mul-1-neg 30.9%

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

      2. associate-/l* 45.5%

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

      3. distribute-lft-neg-out 45.5%

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

      4. *-commutative 45.5%

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

   7. Simplified 45.5%

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

   8. Taylor expanded in z around inf 52.0%

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

      1. associate-/l* 59.7%

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

   10. Simplified 59.7%

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

   11. Taylor expanded in t around 0 60.1%

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

       1. neg-mul-1 60.1%

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

   13. Simplified 60.1%

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

   14. Taylor expanded in t around inf 48.9%

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

   if -3.4999999999999998e99 < z < 3.0999999999999998e-307

   1. Initial program 77.5%

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

      1. +-commutative 77.5%

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

      2. *-commutative 77.5%

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

      3. associate-/l* 87.3%

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

      4. fma-define 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in a around inf 34.3%

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

   if 3.0999999999999998e-307 < z < 14500

   1. Initial program 88.3%

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

      1. +-commutative 88.3%

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

      2. *-commutative 88.3%

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

      3. associate-/l* 92.1%

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

      4. fma-define 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in t around inf 76.8%

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

   6. Taylor expanded in x around 0 53.7%

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

      1. div-sub 53.7%

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

   8. Simplified 53.7%

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

   9. Taylor expanded in z around 0 35.0%

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

       1. associate-/l* 55.3%

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

   11. Simplified 40.0%

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

Alternative 11: 65.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-105} \lor \neg \left(z \leq 2.8 \cdot 10^{-48}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.3e-105) (not (<= z 2.8e-48)))
   (* t (/ (- y z) (- a z)))
   (+ x (* y (/ (- t x) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.3e-105) || !(z <= 2.8e-48)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y * ((t - x) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.3d-105)) .or. (.not. (z <= 2.8d-48))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (y * ((t - x) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.3e-105) || !(z <= 2.8e-48)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y * ((t - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.3e-105) or not (z <= 2.8e-48):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (y * ((t - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.3e-105) || !(z <= 2.8e-48))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.3e-105) || ~((z <= 2.8e-48)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (y * ((t - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.3e-105], N[Not[LessEqual[z, 2.8e-48]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.29999999999999964e-105 or 2.80000000000000005e-48 < z

   1. Initial program 53.8%

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

      1. +-commutative 53.8%

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

      2. *-commutative 53.8%

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

      3. associate-/l* 74.9%

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

      4. fma-define 74.9%

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

   3. Simplified 74.9%

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

   5. Taylor expanded in t around inf 65.7%

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

   6. Taylor expanded in x around 0 61.6%

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

      1. div-sub 61.6%

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

   8. Simplified 61.6%

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

   if -4.29999999999999964e-105 < z < 2.80000000000000005e-48

   1. Initial program 93.0%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in z around 0 79.9%

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

      1. associate-/l* 81.2%

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

   7. Simplified 81.2%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-105} \lor \neg \left(z \leq 2.8 \cdot 10^{-48}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-127} \lor \neg \left(t \leq 6.5 \cdot 10^{-63}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z - a} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.2e-127) (not (<= t 6.5e-63)))
   (* t (/ (- y z) (- a z)))
   (* x (+ (/ y (- z a)) 1.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.2e-127) || !(t <= 6.5e-63)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * ((y / (z - a)) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.2d-127)) .or. (.not. (t <= 6.5d-63))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x * ((y / (z - a)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.2e-127) || !(t <= 6.5e-63)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * ((y / (z - a)) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.2e-127) or not (t <= 6.5e-63):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x * ((y / (z - a)) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.2e-127) || !(t <= 6.5e-63))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x * Float64(Float64(y / Float64(z - a)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.2e-127) || ~((t <= 6.5e-63)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x * ((y / (z - a)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.2e-127], N[Not[LessEqual[t, 6.5e-63]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.20000000000000017e-127 or 6.4999999999999998e-63 < t

   1. Initial program 64.2%

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

      1. +-commutative 64.2%

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

      2. *-commutative 64.2%

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

      3. associate-/l* 86.2%

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

      4. fma-define 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in t around inf 75.3%

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

   6. Taylor expanded in x around 0 72.1%

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

      1. div-sub 72.1%

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

   8. Simplified 72.1%

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

   if -3.20000000000000017e-127 < t < 6.4999999999999998e-63

   1. Initial program 64.5%

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

      1. associate-/l* 61.8%

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

   3. Simplified 61.8%

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

   5. Taylor expanded in y around inf 59.5%

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

      1. associate-*r/ 59.5%

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

   7. Simplified 59.5%

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

   8. Taylor expanded in x around inf 53.8%

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

      1. mul-1-neg 53.8%

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

      2. unsub-neg 53.8%

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

   10. Simplified 53.8%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-127} \lor \neg \left(t \leq 6.5 \cdot 10^{-63}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z - a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-128} \lor \neg \left(t \leq 9.5 \cdot 10^{-63}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.5e-128) (not (<= t 9.5e-63)))
   (* t (/ (- y z) (- a z)))
   (* x (- 1.0 (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.5e-128) || !(t <= 9.5e-63)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-5.5d-128)) .or. (.not. (t <= 9.5d-63))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x * (1.0d0 - (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.5e-128) || !(t <= 9.5e-63)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.5e-128) or not (t <= 9.5e-63):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.5e-128) || !(t <= 9.5e-63))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5.5e-128) || ~((t <= 9.5e-63)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.5e-128], N[Not[LessEqual[t, 9.5e-63]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.5000000000000004e-128 or 9.50000000000000016e-63 < t

   1. Initial program 64.2%

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

      1. +-commutative 64.2%

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

      2. *-commutative 64.2%

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

      3. associate-/l* 86.2%

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

      4. fma-define 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in t around inf 75.3%

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

   6. Taylor expanded in x around 0 72.1%

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

      1. div-sub 72.1%

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

   8. Simplified 72.1%

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

   if -5.5000000000000004e-128 < t < 9.50000000000000016e-63

   1. Initial program 64.5%

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

      1. associate-/l* 61.8%

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

   3. Simplified 61.8%

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

   5. Taylor expanded in z around 0 50.0%

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

   6. Taylor expanded in x around inf 50.0%

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

      1. mul-1-neg 50.0%

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

      2. unsub-neg 50.0%

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

   8. Simplified 50.0%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-128} \lor \neg \left(t \leq 9.5 \cdot 10^{-63}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 64.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+34}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.1e+34)
   (+ x (* y (/ (- t x) a)))
   (if (<= a 2.2e+80) (* t (/ (- y z) (- a z))) (+ x (/ t (/ a (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.1e+34) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= 2.2e+80) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (t / (a / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.1d+34)) then
        tmp = x + (y * ((t - x) / a))
    else if (a <= 2.2d+80) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (t / (a / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.1e+34) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= 2.2e+80) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (t / (a / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.1e+34:
		tmp = x + (y * ((t - x) / a))
	elif a <= 2.2e+80:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (t / (a / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.1e+34)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (a <= 2.2e+80)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(t / Float64(a / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.1e+34)
		tmp = x + (y * ((t - x) / a));
	elseif (a <= 2.2e+80)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (t / (a / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.1e+34], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e+80], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.10000000000000017e34

   1. Initial program 65.3%

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

      1. associate-/l* 85.0%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in z around 0 56.4%

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

      1. associate-/l* 66.2%

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

   7. Simplified 66.2%

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

   if -2.10000000000000017e34 < a < 2.20000000000000003e80

   1. Initial program 65.4%

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

      1. +-commutative 65.4%

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

      2. *-commutative 65.4%

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

      3. associate-/l* 74.3%

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

      4. fma-define 74.3%

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

   3. Simplified 74.3%

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

   5. Taylor expanded in t around inf 69.1%

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

   6. Taylor expanded in x around 0 67.0%

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

      1. div-sub 67.0%

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

   8. Simplified 67.0%

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

   if 2.20000000000000003e80 < a

   1. Initial program 59.5%

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

      1. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in y around 0 72.0%

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

      1. mul-1-neg 72.0%

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

      2. associate-/l* 87.5%

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

      3. distribute-lft-neg-out 87.5%

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

      4. +-commutative 87.5%

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

      5. div-sub 87.5%

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

      6. distribute-rgt-out 87.5%

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

      7. sub-neg 87.5%

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

      8. associate-/r/ 91.3%

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

   7. Simplified 91.3%

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

   8. Taylor expanded in t around inf 85.1%

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

   9. Taylor expanded in a around inf 72.2%

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

Alternative 15: 55.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+49} \lor \neg \left(a \leq 9.8 \cdot 10^{-26}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.8e+49) (not (<= a 9.8e-26)))
   (+ x (* t (/ y a)))
   (* t (/ (- z y) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.8e+49) || !(a <= 9.8e-26)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t * ((z - y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.8d+49)) .or. (.not. (a <= 9.8d-26))) then
        tmp = x + (t * (y / a))
    else
        tmp = t * ((z - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.8e+49) || !(a <= 9.8e-26)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t * ((z - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.8e+49) or not (a <= 9.8e-26):
		tmp = x + (t * (y / a))
	else:
		tmp = t * ((z - y) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.8e+49) || !(a <= 9.8e-26))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(t * Float64(Float64(z - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.8e+49) || ~((a <= 9.8e-26)))
		tmp = x + (t * (y / a));
	else
		tmp = t * ((z - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.8e+49], N[Not[LessEqual[a, 9.8e-26]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.7999999999999999e49 or 9.7999999999999998e-26 < a

   1. Initial program 66.0%

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

      1. associate-/l* 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in t around inf 61.4%

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

      1. associate-/l* 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in z around 0 49.6%

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

      1. associate-/l* 55.9%

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

   10. Simplified 55.9%

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

   if -3.7999999999999999e49 < a < 9.7999999999999998e-26

   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. *-commutative 62.9%

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

      3. associate-/l* 72.8%

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

      4. fma-define 72.9%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in t around inf 66.4%

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

   6. Taylor expanded in x around 0 66.8%

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

      1. div-sub 66.8%

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

   8. Simplified 66.8%

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

   9. Taylor expanded in a around 0 57.3%

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

       1. associate-*r/ 57.3%

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

       2. neg-mul-1 57.3%

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

   11. Simplified 57.3%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+49} \lor \neg \left(a \leq 9.8 \cdot 10^{-26}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 56.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+65} \lor \neg \left(z \leq 2.3 \cdot 10^{+20}\right):\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.65e+65) (not (<= z 2.3e+20)))
   (- t (* a (/ x z)))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.65e+65) || !(z <= 2.3e+20)) {
		tmp = t - (a * (x / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.65d+65)) .or. (.not. (z <= 2.3d+20))) then
        tmp = t - (a * (x / z))
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.65e+65) || !(z <= 2.3e+20)) {
		tmp = t - (a * (x / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.65e+65) or not (z <= 2.3e+20):
		tmp = t - (a * (x / z))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.65e+65) || !(z <= 2.3e+20))
		tmp = Float64(t - Float64(a * Float64(x / z)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.65e+65) || ~((z <= 2.3e+20)))
		tmp = t - (a * (x / z));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.65e+65], N[Not[LessEqual[z, 2.3e+20]], $MachinePrecision]], N[(t - N[(a * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.65000000000000011e65 or 2.3e20 < z

   1. Initial program 43.1%

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

      1. associate-/l* 60.4%

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

   3. Simplified 60.4%

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

   5. Taylor expanded in y around 0 28.6%

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

      1. mul-1-neg 28.6%

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

      2. associate-/l* 42.9%

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

      3. distribute-lft-neg-out 42.9%

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

      4. *-commutative 42.9%

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

   7. Simplified 42.9%

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

   8. Taylor expanded in z around inf 51.2%

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

      1. associate-/l* 58.4%

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

   10. Simplified 58.4%

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

   11. Taylor expanded in t around 0 58.7%

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

       1. neg-mul-1 58.7%

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

   13. Simplified 58.7%

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

       1. *-commutative 58.7%

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

       2. add-sqr-sqrt 30.9%

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

       3. sqrt-unprod 44.7%

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

       4. sqr-neg 44.7%

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

       5. sqrt-unprod 24.6%

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

       6. add-sqr-sqrt 46.7%

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

       7. cancel-sign-sub 46.7%

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

       8. distribute-frac-neg 46.7%

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

       9. *-commutative 46.7%

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

       10. add-sqr-sqrt 22.1%

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

       11. sqrt-unprod 42.8%

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

       12. sqr-neg 42.8%

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

       13. sqrt-unprod 27.8%

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

       14. add-sqr-sqrt 58.7%

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

   15. Applied egg-rr 58.7%

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

   if -2.65000000000000011e65 < z < 2.3e20

   1. Initial program 83.4%

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

      1. associate-/l* 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in t around inf 69.3%

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

      1. associate-/l* 74.8%

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

   7. Simplified 74.8%

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

   8. Taylor expanded in z around 0 47.6%

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

      1. associate-/l* 52.1%

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

   10. Simplified 52.1%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+65} \lor \neg \left(z \leq 2.3 \cdot 10^{+20}\right):\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 44.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -33000000000000 \lor \neg \left(a \leq 1.7 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -33000000000000.0) (not (<= a 1.7e-16)))
   (* x (- 1.0 (/ y a)))
   (+ t (* a (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -33000000000000.0) || !(a <= 1.7e-16)) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t + (a * (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-33000000000000.0d0)) .or. (.not. (a <= 1.7d-16))) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t + (a * (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -33000000000000.0) || !(a <= 1.7e-16)) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t + (a * (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -33000000000000.0) or not (a <= 1.7e-16):
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t + (a * (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -33000000000000.0) || !(a <= 1.7e-16))
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = Float64(t + Float64(a * Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -33000000000000.0) || ~((a <= 1.7e-16)))
		tmp = x * (1.0 - (y / a));
	else
		tmp = t + (a * (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -33000000000000.0], N[Not[LessEqual[a, 1.7e-16]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.3e13 or 1.7e-16 < a

   1. Initial program 65.3%

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

      1. associate-/l* 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in z around 0 53.4%

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

   6. Taylor expanded in x around inf 47.7%

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

      1. mul-1-neg 47.7%

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

      2. unsub-neg 47.7%

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

   8. Simplified 47.7%

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

   if -3.3e13 < a < 1.7e-16

   1. Initial program 63.4%

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

      1. associate-/l* 66.7%

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

   3. Simplified 66.7%

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

   5. Taylor expanded in y around 0 22.0%

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

      1. mul-1-neg 22.0%

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

      2. associate-/l* 31.8%

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

      3. distribute-lft-neg-out 31.8%

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

      4. *-commutative 31.8%

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

   7. Simplified 31.8%

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

   8. Taylor expanded in z around inf 48.8%

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

      1. associate-/l* 52.3%

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

   10. Simplified 52.3%

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

   11. Taylor expanded in t around inf 41.8%

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

       1. associate-/l* 44.8%

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

   13. Simplified 44.8%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -33000000000000 \lor \neg \left(a \leq 1.7 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 41.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-14} \lor \neg \left(y \leq 3 \cdot 10^{+176}\right):\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -6.5e-14) (not (<= y 3e+176))) (* t (/ y (- a z))) (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6.5e-14) || !(y <= 3e+176)) {
		tmp = t * (y / (a - z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-6.5d-14)) .or. (.not. (y <= 3d+176))) then
        tmp = t * (y / (a - z))
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6.5e-14) || !(y <= 3e+176)) {
		tmp = t * (y / (a - z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -6.5e-14) or not (y <= 3e+176):
		tmp = t * (y / (a - z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -6.5e-14) || !(y <= 3e+176))
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -6.5e-14) || ~((y <= 3e+176)))
		tmp = t * (y / (a - z));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -6.5e-14], N[Not[LessEqual[y, 3e+176]], $MachinePrecision]], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5000000000000001e-14 or 3e176 < y

   1. Initial program 69.0%

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

      1. associate-/l* 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in t around inf 53.7%

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

      1. associate-/l* 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in y around inf 49.7%

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

   9. Taylor expanded in x around 0 39.2%

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

       1. associate-/l* 45.2%

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

   11. Simplified 45.2%

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

   if -6.5000000000000001e-14 < y < 3e176

   1. Initial program 61.5%

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

      1. associate-/l* 70.5%

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

   3. Simplified 70.5%

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

   5. Taylor expanded in t around inf 54.8%

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

      1. associate-/l* 67.1%

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

   7. Simplified 67.1%

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

   8. Taylor expanded in z around inf 43.2%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-14} \lor \neg \left(y \leq 3 \cdot 10^{+176}\right):\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 53.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+157}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+107}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.75e+157)
   t
   (if (<= z 2.5e+107) (+ x (* t (/ y a))) (+ t (/ a (/ z x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.75e+157) {
		tmp = t;
	} else if (z <= 2.5e+107) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t + (a / (z / 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 (z <= (-2.75d+157)) then
        tmp = t
    else if (z <= 2.5d+107) then
        tmp = x + (t * (y / a))
    else
        tmp = t + (a / (z / 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 (z <= -2.75e+157) {
		tmp = t;
	} else if (z <= 2.5e+107) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t + (a / (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.75e+157:
		tmp = t
	elif z <= 2.5e+107:
		tmp = x + (t * (y / a))
	else:
		tmp = t + (a / (z / x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.75e+157)
		tmp = t;
	elseif (z <= 2.5e+107)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(t + Float64(a / Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.75e+157)
		tmp = t;
	elseif (z <= 2.5e+107)
		tmp = x + (t * (y / a));
	else
		tmp = t + (a / (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.75e+157], t, If[LessEqual[z, 2.5e+107], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(a / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7500000000000001e157

   1. Initial program 35.7%

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

      1. associate-/l* 54.2%

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

   3. Simplified 54.2%

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

   5. Taylor expanded in y around 0 30.6%

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

      1. mul-1-neg 30.6%

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

      2. associate-/l* 47.1%

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

      3. distribute-lft-neg-out 47.1%

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

      4. *-commutative 47.1%

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

   7. Simplified 47.1%

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

   8. Taylor expanded in z around inf 57.7%

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

      1. associate-/l* 73.0%

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

   10. Simplified 73.0%

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

   11. Taylor expanded in t around 0 73.2%

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

       1. neg-mul-1 73.2%

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

   13. Simplified 73.2%

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

   14. Taylor expanded in t around inf 61.2%

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

   if -2.7500000000000001e157 < z < 2.5000000000000001e107

   1. Initial program 75.4%

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

      1. associate-/l* 84.2%

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

   3. Simplified 84.2%

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

   5. Taylor expanded in t around inf 63.5%

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

      1. associate-/l* 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in z around 0 42.8%

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

      1. associate-/l* 46.7%

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

   10. Simplified 46.7%

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

   if 2.5000000000000001e107 < z

   1. Initial program 39.3%

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

      1. associate-/l* 56.5%

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

   3. Simplified 56.5%

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

   5. Taylor expanded in y around 0 23.0%

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

      1. mul-1-neg 23.0%

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

      2. associate-/l* 34.0%

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

      3. distribute-lft-neg-out 34.0%

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

      4. *-commutative 34.0%

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

   7. Simplified 34.0%

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

   8. Taylor expanded in z around inf 60.9%

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

      1. associate-/l* 67.2%

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

   10. Simplified 67.2%

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

   11. Taylor expanded in t around 0 67.6%

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

       1. neg-mul-1 67.6%

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

   13. Simplified 67.6%

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

       1. clear-num 67.6%

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

       2. un-div-inv 67.5%

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

       3. add-sqr-sqrt 34.1%

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

       4. sqrt-unprod 47.9%

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

       5. sqr-neg 47.9%

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

       6. sqrt-unprod 30.2%

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

       7. add-sqr-sqrt 58.4%

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

   15. Applied egg-rr 58.4%

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

Alternative 20: 38.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+80}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.2e+49) x (if (<= a 2.6e+80) t (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.2e+49) {
		tmp = x;
	} else if (a <= 2.6e+80) {
		tmp = t;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.2d+49)) then
        tmp = x
    else if (a <= 2.6d+80) then
        tmp = t
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.2e+49) {
		tmp = x;
	} else if (a <= 2.6e+80) {
		tmp = t;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.2e+49:
		tmp = x
	elif a <= 2.6e+80:
		tmp = t
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.2e+49)
		tmp = x;
	elseif (a <= 2.6e+80)
		tmp = t;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.2e+49)
		tmp = x;
	elseif (a <= 2.6e+80)
		tmp = t;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.2e+49], x, If[LessEqual[a, 2.6e+80], t, N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.20000000000000022e49

   1. Initial program 66.3%

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

      1. +-commutative 66.3%

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

      2. *-commutative 66.3%

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

      3. associate-/l* 90.4%

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

      4. fma-define 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in a around inf 41.3%

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

   if -4.20000000000000022e49 < a < 2.59999999999999982e80

   1. Initial program 65.1%

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

      1. associate-/l* 68.8%

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

   3. Simplified 68.8%

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

   5. Taylor expanded in y around 0 23.8%

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

      1. mul-1-neg 23.8%

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

      2. associate-/l* 32.8%

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

      3. distribute-lft-neg-out 32.8%

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

      4. *-commutative 32.8%

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

   7. Simplified 32.8%

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

   8. Taylor expanded in z around inf 43.8%

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

      1. associate-/l* 48.4%

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

   10. Simplified 48.4%

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

   11. Taylor expanded in t around 0 45.6%

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

       1. neg-mul-1 45.6%

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

   13. Simplified 45.6%

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

   14. Taylor expanded in t around inf 37.4%

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

   if 2.59999999999999982e80 < a

   1. Initial program 59.5%

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

      1. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in t around inf 59.9%

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

      1. associate-/l* 85.1%

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

   7. Simplified 85.1%

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

   8. Taylor expanded in z around inf 48.5%

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

Alternative 21: 39.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+80}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.9e+49) x (if (<= a 4e+80) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.9e+49) {
		tmp = x;
	} else if (a <= 4e+80) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.9d+49)) then
        tmp = x
    else if (a <= 4d+80) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.9e+49) {
		tmp = x;
	} else if (a <= 4e+80) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.9e+49:
		tmp = x
	elif a <= 4e+80:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.9e+49)
		tmp = x;
	elseif (a <= 4e+80)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.9e+49)
		tmp = x;
	elseif (a <= 4e+80)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.9e+49], x, If[LessEqual[a, 4e+80], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.9000000000000001e49 or 4e80 < a

   1. Initial program 63.2%

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

      1. +-commutative 63.2%

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

      2. *-commutative 63.2%

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

      3. associate-/l* 90.8%

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

      4. fma-define 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in a around inf 43.6%

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

   if -3.9000000000000001e49 < a < 4e80

   1. Initial program 65.1%

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

      1. associate-/l* 68.8%

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

   3. Simplified 68.8%

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

   5. Taylor expanded in y around 0 23.8%

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

      1. mul-1-neg 23.8%

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

      2. associate-/l* 32.8%

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

      3. distribute-lft-neg-out 32.8%

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

      4. *-commutative 32.8%

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

   7. Simplified 32.8%

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

   8. Taylor expanded in z around inf 43.8%

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

      1. associate-/l* 48.4%

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

   10. Simplified 48.4%

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

   11. Taylor expanded in t around 0 45.6%

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

       1. neg-mul-1 45.6%

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

   13. Simplified 45.6%

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

   14. Taylor expanded in t around inf 37.4%

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

Alternative 22: 25.3% 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 64.3%

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

   1. associate-/l* 75.8%

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

3. Simplified 75.8%

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

5. Taylor expanded in y around 0 33.8%

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

   1. mul-1-neg 33.8%

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

   2. associate-/l* 43.4%

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

   3. distribute-lft-neg-out 43.4%

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

   4. *-commutative 43.4%

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

7. Simplified 43.4%

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

8. Taylor expanded in z around inf 33.2%

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

   1. associate-/l* 38.3%

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

10. Simplified 38.3%

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

11. Taylor expanded in t around 0 36.7%

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

    1. neg-mul-1 36.7%

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

13. Simplified 36.7%

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

14. Taylor expanded in t around inf 28.3%

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

Alternative 23: 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 64.3%

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

   1. associate-/l* 75.8%

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

3. Simplified 75.8%

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

5. Taylor expanded in y around 0 33.8%

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

   1. mul-1-neg 33.8%

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

   2. associate-/l* 43.4%

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

   3. distribute-lft-neg-out 43.4%

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

   4. *-commutative 43.4%

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

7. Simplified 43.4%

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

8. Taylor expanded in a around 0 20.8%

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

   1. associate-*r/ 20.8%

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

   2. neg-mul-1 20.8%

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

   3. sub-neg 20.8%

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

   4. +-commutative 20.8%

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

   5. distribute-neg-in 20.8%

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

   6. remove-double-neg 20.8%

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

10. Simplified 20.8%

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

11. Taylor expanded in t around 0 2.8%

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

    1. distribute-rgt1-in 2.8%

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

    2. metadata-eval 2.8%

       \[\leadsto \color{blue}{0} \cdot x \]

    3. mul0-lft 2.8%

       \[\leadsto \color{blue}{0} \]

13. Simplified 2.8%

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

Developer Target 1: 83.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024139 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

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

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