Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.5% → 93.1%

Time: 17.5s

Alternatives: 21

Speedup: 0.3×

Specification

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 80.5% accurate, 1.0× speedup

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 93.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-292} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-292) (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 <= -2e-292) || !(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(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -2e-292) || !(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-292], 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 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.0000000000000001e-292 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.4%

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

      1. +-commutative 90.4%

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

      2. remove-double-neg 90.4%

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

      3. unsub-neg 90.4%

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

      4. *-commutative 90.4%

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

      5. associate-*l/ 78.8%

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

      6. associate-/l* 93.9%

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

      7. fma-neg 93.9%

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

      8. remove-double-neg 93.9%

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

   3. Simplified 93.9%

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

   if -2.0000000000000001e-292 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.3%

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

      1. +-commutative 3.3%

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

      2. remove-double-neg 3.3%

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

      3. unsub-neg 3.3%

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

      4. *-commutative 3.3%

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

      5. associate-*l/ 3.9%

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

      6. associate-/l* 3.3%

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

      7. fma-neg 3.3%

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

      8. remove-double-neg 3.3%

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

   3. Simplified 3.3%

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

   5. Taylor expanded in z around inf 89.6%

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

      1. associate--l+ 89.6%

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

      2. associate-*r/ 89.6%

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

      3. associate-*r/ 89.6%

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

      4. mul-1-neg 89.6%

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

      5. div-sub 89.6%

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

      6. mul-1-neg 89.6%

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

      7. distribute-lft-out-- 89.6%

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

      8. associate-*r/ 89.6%

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

      9. mul-1-neg 89.6%

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

      10. unsub-neg 89.6%

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

      11. distribute-rgt-out-- 89.6%

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

   7. Simplified 89.6%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-292} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t - x}}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -0.0001:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-292}:\\ \;\;\;\;x + t \cdot \left(\frac{y - z}{a - z} + \frac{x}{t} \cdot \frac{y - z}{z - a}\right)\\ \mathbf{elif}\;t\_2 \leq 10^{-285}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ (- a z) (- t x)))))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -0.0001)
     t_1
     (if (<= t_2 -2e-292)
       (+ x (* t (+ (/ (- y z) (- a z)) (* (/ x t) (/ (- y z) (- z a))))))
       (if (<= t_2 1e-285) (- t (/ (* (- t x) (- y a)) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / (t - x)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -0.0001) {
		tmp = t_1;
	} else if (t_2 <= -2e-292) {
		tmp = x + (t * (((y - z) / (a - z)) + ((x / t) * ((y - z) / (z - a)))));
	} else if (t_2 <= 1e-285) {
		tmp = t - (((t - x) * (y - 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) :: t_2
    real(8) :: tmp
    t_1 = x + ((y - z) / ((a - z) / (t - x)))
    t_2 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_2 <= (-0.0001d0)) then
        tmp = t_1
    else if (t_2 <= (-2d-292)) then
        tmp = x + (t * (((y - z) / (a - z)) + ((x / t) * ((y - z) / (z - a)))))
    else if (t_2 <= 1d-285) then
        tmp = t - (((t - x) * (y - a)) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / (t - x)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -0.0001) {
		tmp = t_1;
	} else if (t_2 <= -2e-292) {
		tmp = x + (t * (((y - z) / (a - z)) + ((x / t) * ((y - z) / (z - a)))));
	} else if (t_2 <= 1e-285) {
		tmp = t - (((t - x) * (y - a)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / ((a - z) / (t - x)))
	t_2 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_2 <= -0.0001:
		tmp = t_1
	elif t_2 <= -2e-292:
		tmp = x + (t * (((y - z) / (a - z)) + ((x / t) * ((y - z) / (z - a)))))
	elif t_2 <= 1e-285:
		tmp = t - (((t - x) * (y - a)) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -0.0001)
		tmp = t_1;
	elseif (t_2 <= -2e-292)
		tmp = Float64(x + Float64(t * Float64(Float64(Float64(y - z) / Float64(a - z)) + Float64(Float64(x / t) * Float64(Float64(y - z) / Float64(z - a))))));
	elseif (t_2 <= 1e-285)
		tmp = Float64(t - Float64(Float64(Float64(t - x) * Float64(y - a)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) / ((a - z) / (t - x)));
	t_2 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_2 <= -0.0001)
		tmp = t_1;
	elseif (t_2 <= -2e-292)
		tmp = x + (t * (((y - z) / (a - z)) + ((x / t) * ((y - z) / (z - a)))));
	elseif (t_2 <= 1e-285)
		tmp = t - (((t - x) * (y - 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[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -0.0001], t$95$1, If[LessEqual[t$95$2, -2e-292], N[(x + N[(t * N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(N[(x / t), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e-285], N[(t - N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000005e-4 or 1.00000000000000007e-285 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 93.5%

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

      1. clear-num 93.4%

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

      2. un-div-inv 93.6%

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

   4. Applied egg-rr 93.6%

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

   if -1.00000000000000005e-4 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.0000000000000001e-292

   1. Initial program 66.6%

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

   3. Taylor expanded in t around inf 87.3%

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

      1. associate--l+ 87.3%

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

      2. mul-1-neg 87.3%

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

      3. times-frac 87.5%

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

      4. div-sub 87.6%

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

   5. Simplified 87.6%

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

   if -2.0000000000000001e-292 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.00000000000000007e-285

   1. Initial program 3.4%

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

      1. +-commutative 3.4%

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

      2. remove-double-neg 3.4%

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

      3. unsub-neg 3.4%

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

      4. *-commutative 3.4%

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

      5. associate-*l/ 7.2%

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

      6. associate-/l* 6.7%

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

      7. fma-neg 6.7%

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

      8. remove-double-neg 6.7%

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

   3. Simplified 6.7%

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

   5. Taylor expanded in z around inf 90.0%

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

      1. associate--l+ 90.0%

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

      2. associate-*r/ 90.0%

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

      3. associate-*r/ 90.0%

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

      4. mul-1-neg 90.0%

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

      5. div-sub 90.0%

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

      6. mul-1-neg 90.0%

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

      7. distribute-lft-out-- 90.0%

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

      8. associate-*r/ 90.0%

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

      9. mul-1-neg 90.0%

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

      10. unsub-neg 90.0%

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

      11. distribute-rgt-out-- 90.0%

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

   7. Simplified 90.0%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -0.0001:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-292}:\\ \;\;\;\;x + t \cdot \left(\frac{y - z}{a - z} + \frac{x}{t} \cdot \frac{y - z}{z - a}\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-285}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-292} \lor \neg \left(t\_1 \leq 10^{-285}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-292) (not (<= t_1 1e-285)))
     t_1
     (- 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 <= -2e-292) || !(t_1 <= 1e-285)) {
		tmp = t_1;
	} 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 <= (-2d-292)) .or. (.not. (t_1 <= 1d-285))) then
        tmp = t_1
    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 <= -2e-292) || !(t_1 <= 1e-285)) {
		tmp = t_1;
	} 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 <= -2e-292) or not (t_1 <= 1e-285):
		tmp = t_1
	else:
		tmp = t - (((t - x) * (y - a)) / z)
	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))))
	tmp = 0.0
	if ((t_1 <= -2e-292) || !(t_1 <= 1e-285))
		tmp = t_1;
	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 <= -2e-292) || ~((t_1 <= 1e-285)))
		tmp = t_1;
	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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-292], N[Not[LessEqual[t$95$1, 1e-285]], $MachinePrecision]], t$95$1, 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 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.0000000000000001e-292 or 1.00000000000000007e-285 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.8%

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

   if -2.0000000000000001e-292 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.00000000000000007e-285

   1. Initial program 3.4%

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

      1. +-commutative 3.4%

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

      2. remove-double-neg 3.4%

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

      3. unsub-neg 3.4%

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

      4. *-commutative 3.4%

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

      5. associate-*l/ 7.2%

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

      6. associate-/l* 6.7%

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

      7. fma-neg 6.7%

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

      8. remove-double-neg 6.7%

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

   3. Simplified 6.7%

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

   5. Taylor expanded in z around inf 90.0%

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

      1. associate--l+ 90.0%

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

      2. associate-*r/ 90.0%

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

      3. associate-*r/ 90.0%

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

      4. mul-1-neg 90.0%

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

      5. div-sub 90.0%

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

      6. mul-1-neg 90.0%

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

      7. distribute-lft-out-- 90.0%

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

      8. associate-*r/ 90.0%

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

      9. mul-1-neg 90.0%

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

      10. unsub-neg 90.0%

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

      11. distribute-rgt-out-- 90.0%

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

   7. Simplified 90.0%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-292} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-285}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-292}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{-285}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -2e-292)
     t_1
     (if (<= t_1 1e-285)
       (- t (/ (* (- t x) (- y a)) z))
       (+ x (/ (- y z) (/ (- a z) (- t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -2e-292) {
		tmp = t_1;
	} else if (t_1 <= 1e-285) {
		tmp = t - (((t - x) * (y - a)) / z);
	} else {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_1 <= (-2d-292)) then
        tmp = t_1
    else if (t_1 <= 1d-285) then
        tmp = t - (((t - x) * (y - a)) / z)
    else
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -2e-292) {
		tmp = t_1;
	} else if (t_1 <= 1e-285) {
		tmp = t - (((t - x) * (y - a)) / z);
	} else {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -2e-292:
		tmp = t_1
	elif t_1 <= 1e-285:
		tmp = t - (((t - x) * (y - a)) / z)
	else:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	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))))
	tmp = 0.0
	if (t_1 <= -2e-292)
		tmp = t_1;
	elseif (t_1 <= 1e-285)
		tmp = Float64(t - Float64(Float64(Float64(t - x) * Float64(y - a)) / z));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	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 <= -2e-292)
		tmp = t_1;
	elseif (t_1 <= 1e-285)
		tmp = t - (((t - x) * (y - a)) / z);
	else
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	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]}, If[LessEqual[t$95$1, -2e-292], t$95$1, If[LessEqual[t$95$1, 1e-285], N[(t - N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.0000000000000001e-292

   1. Initial program 90.9%

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

   if -2.0000000000000001e-292 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.00000000000000007e-285

   1. Initial program 3.4%

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

      1. +-commutative 3.4%

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

      2. remove-double-neg 3.4%

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

      3. unsub-neg 3.4%

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

      4. *-commutative 3.4%

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

      5. associate-*l/ 7.2%

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

      6. associate-/l* 6.7%

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

      7. fma-neg 6.7%

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

      8. remove-double-neg 6.7%

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

   3. Simplified 6.7%

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

   5. Taylor expanded in z around inf 90.0%

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

      1. associate--l+ 90.0%

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

      2. associate-*r/ 90.0%

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

      3. associate-*r/ 90.0%

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

      4. mul-1-neg 90.0%

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

      5. div-sub 90.0%

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

      6. mul-1-neg 90.0%

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

      7. distribute-lft-out-- 90.0%

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

      8. associate-*r/ 90.0%

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

      9. mul-1-neg 90.0%

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

      10. unsub-neg 90.0%

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

      11. distribute-rgt-out-- 90.0%

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

   7. Simplified 90.0%

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

   if 1.00000000000000007e-285 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.7%

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

      1. clear-num 90.6%

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

      2. un-div-inv 90.7%

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

   4. Applied egg-rr 90.7%

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

Alternative 5: 63.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{if}\;z \leq -5.7 \cdot 10^{+180}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.0295:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y z) (/ (- a z) t))))
   (if (<= z -5.7e+180)
     (+ t (* a (/ (- t x) z)))
     (if (<= z -1.52e-106)
       t_1
       (if (<= z 0.0295)
         (+ x (/ y (/ a (- t x))))
         (if (<= z 5.3e+116) t_1 (+ t (/ (* x y) z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) / ((a - z) / t);
	double tmp;
	if (z <= -5.7e+180) {
		tmp = t + (a * ((t - x) / z));
	} else if (z <= -1.52e-106) {
		tmp = t_1;
	} else if (z <= 0.0295) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 5.3e+116) {
		tmp = t_1;
	} else {
		tmp = t + ((x * y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) / ((a - z) / t)
    if (z <= (-5.7d+180)) then
        tmp = t + (a * ((t - x) / z))
    else if (z <= (-1.52d-106)) then
        tmp = t_1
    else if (z <= 0.0295d0) then
        tmp = x + (y / (a / (t - x)))
    else if (z <= 5.3d+116) then
        tmp = t_1
    else
        tmp = t + ((x * y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) / ((a - z) / t);
	double tmp;
	if (z <= -5.7e+180) {
		tmp = t + (a * ((t - x) / z));
	} else if (z <= -1.52e-106) {
		tmp = t_1;
	} else if (z <= 0.0295) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 5.3e+116) {
		tmp = t_1;
	} else {
		tmp = t + ((x * y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) / ((a - z) / t)
	tmp = 0
	if z <= -5.7e+180:
		tmp = t + (a * ((t - x) / z))
	elif z <= -1.52e-106:
		tmp = t_1
	elif z <= 0.0295:
		tmp = x + (y / (a / (t - x)))
	elif z <= 5.3e+116:
		tmp = t_1
	else:
		tmp = t + ((x * y) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) / Float64(Float64(a - z) / t))
	tmp = 0.0
	if (z <= -5.7e+180)
		tmp = Float64(t + Float64(a * Float64(Float64(t - x) / z)));
	elseif (z <= -1.52e-106)
		tmp = t_1;
	elseif (z <= 0.0295)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (z <= 5.3e+116)
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(x * y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) / ((a - z) / t);
	tmp = 0.0;
	if (z <= -5.7e+180)
		tmp = t + (a * ((t - x) / z));
	elseif (z <= -1.52e-106)
		tmp = t_1;
	elseif (z <= 0.0295)
		tmp = x + (y / (a / (t - x)));
	elseif (z <= 5.3e+116)
		tmp = t_1;
	else
		tmp = t + ((x * y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.7e+180], N[(t + N[(a * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.52e-106], t$95$1, If[LessEqual[z, 0.0295], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.3e+116], t$95$1, N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.7000000000000002e180

   1. Initial program 45.7%

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

   3. Taylor expanded in y around 0 16.2%

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

      1. mul-1-neg 16.2%

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

      2. distribute-neg-frac 16.2%

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

      3. *-commutative 16.2%

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

      4. distribute-rgt-neg-out 16.2%

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

   5. Simplified 16.2%

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

   6. Taylor expanded in z around inf 61.7%

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

      1. associate-*r/ 71.3%

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

   8. Simplified 71.3%

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

   if -5.7000000000000002e180 < z < -1.5200000000000001e-106 or 0.029499999999999998 < z < 5.3000000000000002e116

   1. Initial program 81.1%

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

      1. clear-num 81.0%

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

      2. un-div-inv 81.1%

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

   4. Applied egg-rr 81.1%

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

   5. Taylor expanded in a around 0 81.2%

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

      1. +-commutative 81.2%

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

      2. mul-1-neg 81.2%

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

      3. sub-neg 81.2%

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

   7. Simplified 81.2%

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

   8. Taylor expanded in x around 0 65.7%

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

      1. div-sub 65.7%

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

      2. div-sub 65.7%

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

   10. Simplified 65.7%

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

   if -1.5200000000000001e-106 < z < 0.029499999999999998

   1. Initial program 94.9%

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

      1. clear-num 94.8%

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

      2. un-div-inv 95.0%

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

   4. Applied egg-rr 95.0%

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

   5. Taylor expanded in y around inf 91.0%

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

   6. Taylor expanded in a around inf 81.3%

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

   if 5.3000000000000002e116 < z

   1. Initial program 59.7%

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

   3. Taylor expanded in a around 0 43.8%

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

      1. mul-1-neg 43.8%

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

      2. distribute-neg-frac2 43.8%

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

   5. Simplified 43.8%

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

   6. Taylor expanded in y around 0 70.9%

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

      1. div-sub 70.9%

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

      2. associate-*r* 70.9%

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

      3. mul-1-neg 70.9%

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

   8. Simplified 70.9%

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

   9. Taylor expanded in t around 0 71.1%

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

Alternative 6: 62.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+85}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-66}:\\ \;\;\;\;x + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e+85)
   (+ t (* a (/ (- t x) z)))
   (if (<= z -7.5e-66)
     (+ x (* y (/ (- x t) z)))
     (if (<= z 5.6e+24) (+ x (/ y (/ a (- t x)))) (+ t (/ (* x y) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+85) {
		tmp = t + (a * ((t - x) / z));
	} else if (z <= -7.5e-66) {
		tmp = x + (y * ((x - t) / z));
	} else if (z <= 5.6e+24) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t + ((x * y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.5d+85)) then
        tmp = t + (a * ((t - x) / z))
    else if (z <= (-7.5d-66)) then
        tmp = x + (y * ((x - t) / z))
    else if (z <= 5.6d+24) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t + ((x * y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+85) {
		tmp = t + (a * ((t - x) / z));
	} else if (z <= -7.5e-66) {
		tmp = x + (y * ((x - t) / z));
	} else if (z <= 5.6e+24) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t + ((x * y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.5e+85:
		tmp = t + (a * ((t - x) / z))
	elif z <= -7.5e-66:
		tmp = x + (y * ((x - t) / z))
	elif z <= 5.6e+24:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t + ((x * y) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e+85)
		tmp = Float64(t + Float64(a * Float64(Float64(t - x) / z)));
	elseif (z <= -7.5e-66)
		tmp = Float64(x + Float64(y * Float64(Float64(x - t) / z)));
	elseif (z <= 5.6e+24)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t + Float64(Float64(x * y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.5e+85)
		tmp = t + (a * ((t - x) / z));
	elseif (z <= -7.5e-66)
		tmp = x + (y * ((x - t) / z));
	elseif (z <= 5.6e+24)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t + ((x * y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e+85], N[(t + N[(a * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.5e-66], N[(x + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e+24], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.4999999999999994e85

   1. Initial program 59.0%

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

   3. Taylor expanded in y around 0 22.7%

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

      1. mul-1-neg 22.7%

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

      2. distribute-neg-frac 22.7%

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

      3. *-commutative 22.7%

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

      4. distribute-rgt-neg-out 22.7%

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

   5. Simplified 22.7%

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

   6. Taylor expanded in z around inf 55.8%

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

      1. associate-*r/ 63.3%

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

   8. Simplified 63.3%

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

   if -8.4999999999999994e85 < z < -7.49999999999999995e-66

   1. Initial program 88.9%

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

      1. clear-num 88.9%

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

      2. un-div-inv 89.0%

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

   4. Applied egg-rr 89.0%

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

   5. Taylor expanded in y around inf 76.7%

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

   6. Taylor expanded in a around 0 55.6%

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

      1. mul-1-neg 55.6%

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

      2. associate-*r/ 58.9%

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

      3. unsub-neg 58.9%

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

   8. Simplified 58.9%

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

   if -7.49999999999999995e-66 < z < 5.6000000000000003e24

   1. Initial program 92.4%

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

      1. clear-num 92.4%

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

      2. un-div-inv 92.5%

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

   4. Applied egg-rr 92.5%

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

   5. Taylor expanded in y around inf 87.4%

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

   6. Taylor expanded in a around inf 78.4%

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

   if 5.6000000000000003e24 < z

   1. Initial program 68.8%

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

   3. Taylor expanded in a around 0 48.2%

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

      1. mul-1-neg 48.2%

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

      2. distribute-neg-frac2 48.2%

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

   5. Simplified 48.2%

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

   6. Taylor expanded in y around 0 69.7%

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

      1. div-sub 69.7%

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

      2. associate-*r* 69.7%

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

      3. mul-1-neg 69.7%

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

   8. Simplified 69.7%

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

   9. Taylor expanded in t around 0 62.0%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+85}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-66}:\\ \;\;\;\;x + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+72} \lor \neg \left(z \leq 9.5 \cdot 10^{+26}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.05e+72) (not (<= z 9.5e+26)))
   (+ t (* y (/ (- x t) z)))
   (+ x (/ y (/ (- a z) (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.05e+72) || !(z <= 9.5e+26)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + (y / ((a - z) / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.05d+72)) .or. (.not. (z <= 9.5d+26))) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = x + (y / ((a - z) / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.05e+72) || !(z <= 9.5e+26)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + (y / ((a - z) / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.05e+72) or not (z <= 9.5e+26):
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = x + (y / ((a - z) / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.05e+72) || !(z <= 9.5e+26))
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.05e+72) || ~((z <= 9.5e+26)))
		tmp = t + (y * ((x - t) / z));
	else
		tmp = x + (y / ((a - z) / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.05e+72], N[Not[LessEqual[z, 9.5e+26]], $MachinePrecision]], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.04999999999999996e72 or 9.50000000000000054e26 < z

   1. Initial program 64.3%

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

   3. Taylor expanded in a around 0 46.9%

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

      1. mul-1-neg 46.9%

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

      2. distribute-neg-frac2 46.9%

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

   5. Simplified 46.9%

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

   6. Taylor expanded in y around 0 69.6%

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

      1. div-sub 69.6%

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

      2. associate-*r* 69.6%

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

      3. mul-1-neg 69.6%

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

   8. Simplified 69.6%

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

   if -3.04999999999999996e72 < z < 9.50000000000000054e26

   1. Initial program 92.2%

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

      1. clear-num 92.2%

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

      2. un-div-inv 92.3%

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

   4. Applied egg-rr 92.3%

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

   5. Taylor expanded in y around inf 86.4%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+72} \lor \neg \left(z \leq 9.5 \cdot 10^{+26}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+72} \lor \neg \left(z \leq 2.8 \cdot 10^{+27}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3e+72) (not (<= z 2.8e+27)))
   (+ t (* y (/ (- x t) z)))
   (+ x (* y (/ (- t x) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3e+72) || !(z <= 2.8e+27)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + (y * ((t - x) / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3d+72)) .or. (.not. (z <= 2.8d+27))) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = x + (y * ((t - x) / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3e+72) || !(z <= 2.8e+27)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + (y * ((t - x) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3e+72) or not (z <= 2.8e+27):
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = x + (y * ((t - x) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3e+72) || !(z <= 2.8e+27))
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3e+72) || ~((z <= 2.8e+27)))
		tmp = t + (y * ((x - t) / z));
	else
		tmp = x + (y * ((t - x) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3e+72], N[Not[LessEqual[z, 2.8e+27]], $MachinePrecision]], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.00000000000000003e72 or 2.7999999999999999e27 < z

   1. Initial program 64.3%

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

   3. Taylor expanded in a around 0 46.9%

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

      1. mul-1-neg 46.9%

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

      2. distribute-neg-frac2 46.9%

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

   5. Simplified 46.9%

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

   6. Taylor expanded in y around 0 69.6%

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

      1. div-sub 69.6%

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

      2. associate-*r* 69.6%

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

      3. mul-1-neg 69.6%

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

   8. Simplified 69.6%

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

   if -3.00000000000000003e72 < z < 2.7999999999999999e27

   1. Initial program 92.2%

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

   3. Taylor expanded in y around inf 86.4%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+72} \lor \neg \left(z \leq 2.8 \cdot 10^{+27}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+130} \lor \neg \left(x \leq 2.1 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -3.9e+130) (not (<= x 2.1e+54)))
   (* x (+ (/ (- y z) (- z a)) 1.0))
   (+ x (* t (/ (- y z) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -3.9e+130) || !(x <= 2.1e+54)) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else {
		tmp = x + (t * ((y - z) / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-3.9d+130)) .or. (.not. (x <= 2.1d+54))) then
        tmp = x * (((y - z) / (z - a)) + 1.0d0)
    else
        tmp = x + (t * ((y - z) / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -3.9e+130) || !(x <= 2.1e+54)) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else {
		tmp = x + (t * ((y - z) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -3.9e+130) or not (x <= 2.1e+54):
		tmp = x * (((y - z) / (z - a)) + 1.0)
	else:
		tmp = x + (t * ((y - z) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -3.9e+130) || !(x <= 2.1e+54))
		tmp = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0));
	else
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -3.9e+130) || ~((x <= 2.1e+54)))
		tmp = x * (((y - z) / (z - a)) + 1.0);
	else
		tmp = x + (t * ((y - z) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -3.9e+130], N[Not[LessEqual[x, 2.1e+54]], $MachinePrecision]], N[(x * N[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.9000000000000002e130 or 2.09999999999999986e54 < x

   1. Initial program 75.3%

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

      1. +-commutative 75.3%

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

      2. remove-double-neg 75.3%

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

      3. unsub-neg 75.3%

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

      4. *-commutative 75.3%

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

      5. associate-*l/ 62.2%

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

      6. associate-/l* 77.0%

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

      7. fma-neg 77.1%

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

      8. remove-double-neg 77.1%

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

   3. Simplified 77.1%

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

   5. Taylor expanded in t around 0 59.8%

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

      1. mul-1-neg 59.8%

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

      2. *-rgt-identity 59.8%

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

      3. associate-/l* 72.5%

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

      4. distribute-rgt-neg-in 72.5%

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

      5. mul-1-neg 72.5%

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

      6. distribute-lft-in 72.6%

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

      7. mul-1-neg 72.6%

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

      8. unsub-neg 72.6%

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

   7. Simplified 72.6%

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

   if -3.9000000000000002e130 < x < 2.09999999999999986e54

   1. Initial program 83.7%

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

   3. Taylor expanded in t around inf 64.0%

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

      1. associate-/l* 76.2%

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

   5. Simplified 76.2%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+130} \lor \neg \left(x \leq 2.1 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.08 \cdot 10^{-106} \lor \neg \left(z \leq 10^{+26}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.08e-106) (not (<= z 1e+26)))
   (+ t (* y (/ (- x t) z)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.08e-106) || !(z <= 1e+26)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.08d-106)) .or. (.not. (z <= 1d+26))) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.08e-106) || !(z <= 1e+26)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.08e-106) or not (z <= 1e+26):
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.08e-106) || !(z <= 1e+26))
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.08e-106) || ~((z <= 1e+26)))
		tmp = t + (y * ((x - t) / z));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.08e-106], N[Not[LessEqual[z, 1e+26]], $MachinePrecision]], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0800000000000001e-106 or 1.00000000000000005e26 < z

   1. Initial program 68.9%

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

   3. Taylor expanded in a around 0 47.8%

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

      1. mul-1-neg 47.8%

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

      2. distribute-neg-frac2 47.8%

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

   5. Simplified 47.8%

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

   6. Taylor expanded in y around 0 66.5%

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

      1. div-sub 66.5%

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

      2. associate-*r* 66.5%

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

      3. mul-1-neg 66.5%

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

   8. Simplified 66.5%

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

   if -2.0800000000000001e-106 < z < 1.00000000000000005e26

   1. Initial program 93.6%

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

      1. clear-num 93.5%

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

      2. un-div-inv 93.7%

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

   4. Applied egg-rr 93.7%

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

   5. Taylor expanded in y around inf 89.9%

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

   6. Taylor expanded in a around inf 80.6%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.08 \cdot 10^{-106} \lor \neg \left(z \leq 10^{+26}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+75}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e+75)
   (+ t (* a (/ (- t x) z)))
   (if (<= z 2.8e+27) (+ x (/ y (/ a (- t x)))) (+ t (/ (* x y) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+75) {
		tmp = t + (a * ((t - x) / z));
	} else if (z <= 2.8e+27) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t + ((x * y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.15d+75)) then
        tmp = t + (a * ((t - x) / z))
    else if (z <= 2.8d+27) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t + ((x * y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+75) {
		tmp = t + (a * ((t - x) / z));
	} else if (z <= 2.8e+27) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t + ((x * y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.15e+75:
		tmp = t + (a * ((t - x) / z))
	elif z <= 2.8e+27:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t + ((x * y) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e+75)
		tmp = Float64(t + Float64(a * Float64(Float64(t - x) / z)));
	elseif (z <= 2.8e+27)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t + Float64(Float64(x * y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.15e+75)
		tmp = t + (a * ((t - x) / z));
	elseif (z <= 2.8e+27)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t + ((x * y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e+75], N[(t + N[(a * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+27], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1499999999999999e75

   1. Initial program 58.7%

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

   3. Taylor expanded in y around 0 21.9%

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

      1. mul-1-neg 21.9%

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

      2. distribute-neg-frac 21.9%

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

      3. *-commutative 21.9%

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

      4. distribute-rgt-neg-out 21.9%

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

   5. Simplified 21.9%

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

   6. Taylor expanded in z around inf 55.5%

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

      1. associate-*r/ 62.8%

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

   8. Simplified 62.8%

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

   if -1.1499999999999999e75 < z < 2.7999999999999999e27

   1. Initial program 92.3%

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

      1. clear-num 92.3%

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

      2. un-div-inv 92.4%

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

   4. Applied egg-rr 92.4%

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

   5. Taylor expanded in y around inf 86.0%

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

   6. Taylor expanded in a around inf 72.4%

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

   if 2.7999999999999999e27 < z

   1. Initial program 68.8%

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

   3. Taylor expanded in a around 0 48.2%

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

      1. mul-1-neg 48.2%

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

      2. distribute-neg-frac2 48.2%

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

   5. Simplified 48.2%

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

   6. Taylor expanded in y around 0 69.7%

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

      1. div-sub 69.7%

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

      2. associate-*r* 69.7%

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

      3. mul-1-neg 69.7%

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

   8. Simplified 69.7%

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

   9. Taylor expanded in t around 0 62.0%

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

Alternative 12: 62.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+75}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+26}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7e+75)
   (+ t (* a (/ (- t x) z)))
   (if (<= z 4.6e+26) (+ x (* y (/ (- t x) a))) (+ t (/ (* x y) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7e+75) {
		tmp = t + (a * ((t - x) / z));
	} else if (z <= 4.6e+26) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t + ((x * y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7d+75)) then
        tmp = t + (a * ((t - x) / z))
    else if (z <= 4.6d+26) then
        tmp = x + (y * ((t - x) / a))
    else
        tmp = t + ((x * y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7e+75) {
		tmp = t + (a * ((t - x) / z));
	} else if (z <= 4.6e+26) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t + ((x * y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7e+75:
		tmp = t + (a * ((t - x) / z))
	elif z <= 4.6e+26:
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = t + ((x * y) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7e+75)
		tmp = Float64(t + Float64(a * Float64(Float64(t - x) / z)));
	elseif (z <= 4.6e+26)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	else
		tmp = Float64(t + Float64(Float64(x * y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7e+75)
		tmp = t + (a * ((t - x) / z));
	elseif (z <= 4.6e+26)
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t + ((x * y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7e+75], N[(t + N[(a * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+26], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.9999999999999997e75

   1. Initial program 58.7%

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

   3. Taylor expanded in y around 0 21.9%

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

      1. mul-1-neg 21.9%

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

      2. distribute-neg-frac 21.9%

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

      3. *-commutative 21.9%

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

      4. distribute-rgt-neg-out 21.9%

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

   5. Simplified 21.9%

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

   6. Taylor expanded in z around inf 55.5%

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

      1. associate-*r/ 62.8%

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

   8. Simplified 62.8%

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

   if -6.9999999999999997e75 < z < 4.6000000000000001e26

   1. Initial program 92.3%

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

   3. Taylor expanded in z around 0 68.2%

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

      1. associate-/l* 72.3%

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

   5. Simplified 72.3%

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

   if 4.6000000000000001e26 < z

   1. Initial program 68.8%

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

   3. Taylor expanded in a around 0 48.2%

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

      1. mul-1-neg 48.2%

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

      2. distribute-neg-frac2 48.2%

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

   5. Simplified 48.2%

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

   6. Taylor expanded in y around 0 69.7%

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

      1. div-sub 69.7%

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

      2. associate-*r* 69.7%

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

      3. mul-1-neg 69.7%

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

   8. Simplified 69.7%

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

   9. Taylor expanded in t around 0 62.0%

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

Alternative 13: 59.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+75}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+29}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.35e+75)
   (+ t (* a (/ (- t x) z)))
   (if (<= z 5.3e+29) (+ x (* t (/ (- y z) a))) (+ t (/ (* x y) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+75) {
		tmp = t + (a * ((t - x) / z));
	} else if (z <= 5.3e+29) {
		tmp = x + (t * ((y - z) / a));
	} else {
		tmp = t + ((x * y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.35d+75)) then
        tmp = t + (a * ((t - x) / z))
    else if (z <= 5.3d+29) then
        tmp = x + (t * ((y - z) / a))
    else
        tmp = t + ((x * y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+75) {
		tmp = t + (a * ((t - x) / z));
	} else if (z <= 5.3e+29) {
		tmp = x + (t * ((y - z) / a));
	} else {
		tmp = t + ((x * y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.35e+75:
		tmp = t + (a * ((t - x) / z))
	elif z <= 5.3e+29:
		tmp = x + (t * ((y - z) / a))
	else:
		tmp = t + ((x * y) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.35e+75)
		tmp = Float64(t + Float64(a * Float64(Float64(t - x) / z)));
	elseif (z <= 5.3e+29)
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / a)));
	else
		tmp = Float64(t + Float64(Float64(x * y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.35e+75)
		tmp = t + (a * ((t - x) / z));
	elseif (z <= 5.3e+29)
		tmp = x + (t * ((y - z) / a));
	else
		tmp = t + ((x * y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.35e+75], N[(t + N[(a * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.3e+29], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.34999999999999999e75

   1. Initial program 58.7%

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

   3. Taylor expanded in y around 0 21.9%

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

      1. mul-1-neg 21.9%

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

      2. distribute-neg-frac 21.9%

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

      3. *-commutative 21.9%

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

      4. distribute-rgt-neg-out 21.9%

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

   5. Simplified 21.9%

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

   6. Taylor expanded in z around inf 55.5%

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

      1. associate-*r/ 62.8%

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

   8. Simplified 62.8%

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

   if -1.34999999999999999e75 < z < 5.3e29

   1. Initial program 92.4%

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

   3. Taylor expanded in t around inf 67.9%

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

      1. associate-/l* 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in a around inf 56.5%

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

      1. associate-/l* 59.5%

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

   8. Simplified 59.5%

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

   if 5.3e29 < z

   1. Initial program 68.2%

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

   3. Taylor expanded in a around 0 49.1%

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

      1. mul-1-neg 49.1%

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

      2. distribute-neg-frac2 49.1%

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

   5. Simplified 49.1%

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

   6. Taylor expanded in y around 0 71.1%

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

      1. div-sub 71.1%

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

      2. associate-*r* 71.1%

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

      3. mul-1-neg 71.1%

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

   8. Simplified 71.1%

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

   9. Taylor expanded in t around 0 63.2%

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

Alternative 14: 56.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+72}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 0.0049:\\ \;\;\;\;x \cdot \left(\frac{y}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.3e+72)
   (- t (* a (/ x z)))
   (if (<= z 0.0049) (* x (+ (/ y (- z a)) 1.0)) (+ t (/ (* x y) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+72) {
		tmp = t - (a * (x / z));
	} else if (z <= 0.0049) {
		tmp = x * ((y / (z - a)) + 1.0);
	} else {
		tmp = t + ((x * y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.3d+72)) then
        tmp = t - (a * (x / z))
    else if (z <= 0.0049d0) then
        tmp = x * ((y / (z - a)) + 1.0d0)
    else
        tmp = t + ((x * y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+72) {
		tmp = t - (a * (x / z));
	} else if (z <= 0.0049) {
		tmp = x * ((y / (z - a)) + 1.0);
	} else {
		tmp = t + ((x * y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.3e+72:
		tmp = t - (a * (x / z))
	elif z <= 0.0049:
		tmp = x * ((y / (z - a)) + 1.0)
	else:
		tmp = t + ((x * y) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.3e+72)
		tmp = Float64(t - Float64(a * Float64(x / z)));
	elseif (z <= 0.0049)
		tmp = Float64(x * Float64(Float64(y / Float64(z - a)) + 1.0));
	else
		tmp = Float64(t + Float64(Float64(x * y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.3e+72)
		tmp = t - (a * (x / z));
	elseif (z <= 0.0049)
		tmp = x * ((y / (z - a)) + 1.0);
	else
		tmp = t + ((x * y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.3e+72], N[(t - N[(a * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0049], N[(x * N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3e72

   1. Initial program 60.2%

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

   3. Taylor expanded in y around 0 24.8%

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

      1. mul-1-neg 24.8%

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

      2. distribute-neg-frac 24.8%

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

      3. *-commutative 24.8%

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

      4. distribute-rgt-neg-out 24.8%

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

   5. Simplified 24.8%

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

   6. Taylor expanded in z around inf 53.5%

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

   7. Taylor expanded in t around 0 57.1%

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

      1. mul-1-neg 57.1%

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

      2. associate-/l* 60.6%

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

      3. distribute-lft-neg-in 60.6%

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

   9. Simplified 60.6%

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

   if -2.3e72 < z < 0.0048999999999999998

   1. Initial program 93.2%

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

      1. clear-num 93.1%

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

      2. un-div-inv 93.3%

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

   4. Applied egg-rr 93.3%

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

   5. Taylor expanded in y around inf 87.1%

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

   6. Taylor expanded in x around inf 60.9%

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

      1. mul-1-neg 60.9%

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

      2. unsub-neg 60.9%

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

   8. Simplified 60.9%

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

   if 0.0048999999999999998 < z

   1. Initial program 69.3%

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

   3. Taylor expanded in a around 0 46.1%

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

      1. mul-1-neg 46.1%

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

      2. distribute-neg-frac2 46.1%

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

   5. Simplified 46.1%

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

   6. Taylor expanded in y around 0 66.7%

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

      1. div-sub 66.7%

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

      2. associate-*r* 66.7%

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

      3. mul-1-neg 66.7%

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

   8. Simplified 66.7%

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

   9. Taylor expanded in t around 0 57.2%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+72}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 0.0049:\\ \;\;\;\;x \cdot \left(\frac{y}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 38.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+85} \lor \neg \left(z \leq 7.5 \cdot 10^{-5}\right):\\ \;\;\;\;t \cdot \left(\frac{a}{z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.2e+85) (not (<= z 7.5e-5))) (* t (+ (/ a z) 1.0)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.2e+85) || !(z <= 7.5e-5)) {
		tmp = t * ((a / z) + 1.0);
	} 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 ((z <= (-4.2d+85)) .or. (.not. (z <= 7.5d-5))) then
        tmp = t * ((a / z) + 1.0d0)
    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 ((z <= -4.2e+85) || !(z <= 7.5e-5)) {
		tmp = t * ((a / z) + 1.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.2e+85) or not (z <= 7.5e-5):
		tmp = t * ((a / z) + 1.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.2e+85) || !(z <= 7.5e-5))
		tmp = Float64(t * Float64(Float64(a / z) + 1.0));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.2e+85) || ~((z <= 7.5e-5)))
		tmp = t * ((a / z) + 1.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.2e+85], N[Not[LessEqual[z, 7.5e-5]], $MachinePrecision]], N[(t * N[(N[(a / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.2000000000000002e85 or 7.49999999999999934e-5 < z

   1. Initial program 64.8%

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

   3. Taylor expanded in y around 0 28.5%

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

      1. mul-1-neg 28.5%

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

      2. distribute-neg-frac 28.5%

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

      3. *-commutative 28.5%

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

      4. distribute-rgt-neg-out 28.5%

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

   5. Simplified 28.5%

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

   6. Taylor expanded in z around inf 49.2%

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

   7. Taylor expanded in t around inf 45.6%

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

   if -4.2000000000000002e85 < z < 7.49999999999999934e-5

   1. Initial program 92.6%

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

      1. +-commutative 92.6%

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

      2. remove-double-neg 92.6%

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

      3. unsub-neg 92.6%

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

      4. *-commutative 92.6%

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

      5. associate-*l/ 88.7%

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

      6. associate-/l* 93.6%

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

      7. fma-neg 93.7%

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

      8. remove-double-neg 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in a around inf 32.3%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+85} \lor \neg \left(z \leq 7.5 \cdot 10^{-5}\right):\\ \;\;\;\;t \cdot \left(\frac{a}{z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 56.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+74}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+23}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e+74)
   (- t (* a (/ x z)))
   (if (<= z 7.5e+23) (+ x (* t (/ y a))) (+ t (/ (* x y) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+74) {
		tmp = t - (a * (x / z));
	} else if (z <= 7.5e+23) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t + ((x * y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.4d+74)) then
        tmp = t - (a * (x / z))
    else if (z <= 7.5d+23) then
        tmp = x + (t * (y / a))
    else
        tmp = t + ((x * y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+74) {
		tmp = t - (a * (x / z));
	} else if (z <= 7.5e+23) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t + ((x * y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e+74:
		tmp = t - (a * (x / z))
	elif z <= 7.5e+23:
		tmp = x + (t * (y / a))
	else:
		tmp = t + ((x * y) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e+74)
		tmp = Float64(t - Float64(a * Float64(x / z)));
	elseif (z <= 7.5e+23)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(t + Float64(Float64(x * y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.4e+74)
		tmp = t - (a * (x / z));
	elseif (z <= 7.5e+23)
		tmp = x + (t * (y / a));
	else
		tmp = t + ((x * y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e+74], N[(t - N[(a * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+23], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.40000000000000008e74

   1. Initial program 58.7%

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

   3. Taylor expanded in y around 0 21.9%

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

      1. mul-1-neg 21.9%

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

      2. distribute-neg-frac 21.9%

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

      3. *-commutative 21.9%

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

      4. distribute-rgt-neg-out 21.9%

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

   5. Simplified 21.9%

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

   6. Taylor expanded in z around inf 55.5%

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

   7. Taylor expanded in t around 0 59.0%

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

      1. mul-1-neg 59.0%

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

      2. associate-/l* 62.7%

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

      3. distribute-lft-neg-in 62.7%

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

   9. Simplified 62.7%

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

   if -2.40000000000000008e74 < z < 7.49999999999999987e23

   1. Initial program 92.3%

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

   3. Taylor expanded in t around inf 67.7%

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

      1. associate-/l* 70.1%

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

   5. Simplified 70.1%

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

   6. Taylor expanded in z around 0 52.7%

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

      1. associate-/l* 56.3%

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

   8. Simplified 56.3%

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

   if 7.49999999999999987e23 < z

   1. Initial program 68.8%

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

   3. Taylor expanded in a around 0 48.2%

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

      1. mul-1-neg 48.2%

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

      2. distribute-neg-frac2 48.2%

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

   5. Simplified 48.2%

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

   6. Taylor expanded in y around 0 69.7%

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

      1. div-sub 69.7%

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

      2. associate-*r* 69.7%

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

      3. mul-1-neg 69.7%

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

   8. Simplified 69.7%

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

   9. Taylor expanded in t around 0 62.0%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+74}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+23}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 54.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-90}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+27}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.4e-90)
   (* t (- 1.0 (/ y z)))
   (if (<= z 2e+27) (+ x (* t (/ y a))) (+ t (/ (* x y) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.4e-90) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 2e+27) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t + ((x * y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.4d-90)) then
        tmp = t * (1.0d0 - (y / z))
    else if (z <= 2d+27) then
        tmp = x + (t * (y / a))
    else
        tmp = t + ((x * y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.4e-90) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 2e+27) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t + ((x * y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.4e-90:
		tmp = t * (1.0 - (y / z))
	elif z <= 2e+27:
		tmp = x + (t * (y / a))
	else:
		tmp = t + ((x * y) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.4e-90)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (z <= 2e+27)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(t + Float64(Float64(x * y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.4e-90)
		tmp = t * (1.0 - (y / z));
	elseif (z <= 2e+27)
		tmp = x + (t * (y / a));
	else
		tmp = t + ((x * y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.4e-90], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+27], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.39999999999999994e-90

   1. Initial program 68.7%

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

   3. Taylor expanded in a around 0 48.1%

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

      1. mul-1-neg 48.1%

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

      2. distribute-neg-frac2 48.1%

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

   5. Simplified 48.1%

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

   6. Taylor expanded in y around 0 65.2%

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

      1. div-sub 65.2%

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

      2. associate-*r* 65.2%

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

      3. mul-1-neg 65.2%

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

   8. Simplified 65.2%

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

   9. Taylor expanded in t around inf 51.8%

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

       1. mul-1-neg 51.8%

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

       2. unsub-neg 51.8%

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

   11. Simplified 51.8%

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

   if -3.39999999999999994e-90 < z < 2e27

   1. Initial program 93.6%

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

   3. Taylor expanded in t around inf 67.8%

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

      1. associate-/l* 70.1%

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

   5. Simplified 70.1%

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

   6. Taylor expanded in z around 0 57.1%

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

      1. associate-/l* 61.7%

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

   8. Simplified 61.7%

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

   if 2e27 < z

   1. Initial program 68.8%

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

   3. Taylor expanded in a around 0 48.2%

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

      1. mul-1-neg 48.2%

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

      2. distribute-neg-frac2 48.2%

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

   5. Simplified 48.2%

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

   6. Taylor expanded in y around 0 69.7%

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

      1. div-sub 69.7%

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

      2. associate-*r* 69.7%

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

      3. mul-1-neg 69.7%

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

   8. Simplified 69.7%

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

   9. Taylor expanded in t around 0 62.0%

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

Alternative 18: 43.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{-95}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.22e-95)
   (* t (- 1.0 (/ y z)))
   (if (<= z 1.25e-103) x (+ t (/ (* x y) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.22e-95) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 1.25e-103) {
		tmp = x;
	} else {
		tmp = t + ((x * y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.22d-95)) then
        tmp = t * (1.0d0 - (y / z))
    else if (z <= 1.25d-103) then
        tmp = x
    else
        tmp = t + ((x * y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.22e-95) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 1.25e-103) {
		tmp = x;
	} else {
		tmp = t + ((x * y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.22e-95:
		tmp = t * (1.0 - (y / z))
	elif z <= 1.25e-103:
		tmp = x
	else:
		tmp = t + ((x * y) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.22e-95)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (z <= 1.25e-103)
		tmp = x;
	else
		tmp = Float64(t + Float64(Float64(x * y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.22e-95)
		tmp = t * (1.0 - (y / z));
	elseif (z <= 1.25e-103)
		tmp = x;
	else
		tmp = t + ((x * y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.22e-95], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e-103], x, N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.22e-95

   1. Initial program 68.7%

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

   3. Taylor expanded in a around 0 48.1%

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

      1. mul-1-neg 48.1%

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

      2. distribute-neg-frac2 48.1%

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

   5. Simplified 48.1%

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

   6. Taylor expanded in y around 0 65.2%

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

      1. div-sub 65.2%

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

      2. associate-*r* 65.2%

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

      3. mul-1-neg 65.2%

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

   8. Simplified 65.2%

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

   9. Taylor expanded in t around inf 51.8%

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

       1. mul-1-neg 51.8%

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

       2. unsub-neg 51.8%

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

   11. Simplified 51.8%

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

   if -1.22e-95 < z < 1.24999999999999992e-103

   1. Initial program 95.6%

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

      1. +-commutative 95.6%

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

      2. remove-double-neg 95.6%

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

      3. unsub-neg 95.6%

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

      4. *-commutative 95.6%

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

      5. associate-*l/ 90.2%

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

      6. associate-/l* 96.2%

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

      7. fma-neg 96.3%

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

      8. remove-double-neg 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in a around inf 38.0%

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

   if 1.24999999999999992e-103 < z

   1. Initial program 76.5%

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

   3. Taylor expanded in a around 0 44.5%

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

      1. mul-1-neg 44.5%

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

      2. distribute-neg-frac2 44.5%

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

   5. Simplified 44.5%

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

   6. Taylor expanded in y around 0 59.8%

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

      1. div-sub 59.8%

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

      2. associate-*r* 59.8%

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

      3. mul-1-neg 59.8%

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

   8. Simplified 59.8%

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

   9. Taylor expanded in t around 0 51.0%

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

Alternative 19: 47.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+40}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+92}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.2e+40) (+ x t) (if (<= a 2.15e+92) (* t (- 1.0 (/ y z))) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.2e+40) {
		tmp = x + t;
	} else if (a <= 2.15e+92) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.2d+40)) then
        tmp = x + t
    else if (a <= 2.15d+92) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.2e+40) {
		tmp = x + t;
	} else if (a <= 2.15e+92) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.2e+40:
		tmp = x + t
	elif a <= 2.15e+92:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.2e+40)
		tmp = Float64(x + t);
	elseif (a <= 2.15e+92)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.2e+40)
		tmp = x + t;
	elseif (a <= 2.15e+92)
		tmp = t * (1.0 - (y / z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.2e+40], N[(x + t), $MachinePrecision], If[LessEqual[a, 2.15e+92], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if a < -2.1999999999999999e40

   1. Initial program 80.3%

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

   3. Taylor expanded in t around inf 57.0%

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

      1. associate-/l* 70.2%

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

   5. Simplified 70.2%

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

   6. Taylor expanded in z around inf 37.6%

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

   if -2.1999999999999999e40 < a < 2.1499999999999999e92

   1. Initial program 79.3%

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

   3. Taylor expanded in a around 0 51.4%

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

      1. mul-1-neg 51.4%

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

      2. distribute-neg-frac2 51.4%

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

   5. Simplified 51.4%

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

   6. Taylor expanded in y around 0 63.8%

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

      1. div-sub 63.8%

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

      2. associate-*r* 63.8%

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

      3. mul-1-neg 63.8%

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

   8. Simplified 63.8%

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

   9. Taylor expanded in t around inf 48.8%

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

       1. mul-1-neg 48.8%

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

       2. unsub-neg 48.8%

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

   11. Simplified 48.8%

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

   if 2.1499999999999999e92 < a

   1. Initial program 87.9%

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

      1. +-commutative 87.9%

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

      2. remove-double-neg 87.9%

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

      3. unsub-neg 87.9%

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

      4. *-commutative 87.9%

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

      5. associate-*l/ 68.6%

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

      6. associate-/l* 92.4%

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

      7. fma-neg 92.4%

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

      8. remove-double-neg 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in a around inf 48.0%

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

Alternative 20: 38.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+61}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 0.0025:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.7e+61) t (if (<= z 0.0025) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.7e+61) {
		tmp = t;
	} else if (z <= 0.0025) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.7d+61)) then
        tmp = t
    else if (z <= 0.0025d0) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.7e+61) {
		tmp = t;
	} else if (z <= 0.0025) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.7e+61:
		tmp = t
	elif z <= 0.0025:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.7e+61)
		tmp = t;
	elseif (z <= 0.0025)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.7e+61)
		tmp = t;
	elseif (z <= 0.0025)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.7e+61], t, If[LessEqual[z, 0.0025], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -4.6999999999999998e61 or 0.00250000000000000005 < z

   1. Initial program 65.8%

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

      1. clear-num 64.7%

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

      2. un-div-inv 64.9%

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

   4. Applied egg-rr 64.9%

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

   5. Taylor expanded in a around 0 64.6%

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

      1. +-commutative 64.6%

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

      2. mul-1-neg 64.6%

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

      3. sub-neg 64.6%

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

   7. Simplified 64.6%

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

   8. Taylor expanded in z around -inf 42.6%

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

   if -4.6999999999999998e61 < z < 0.00250000000000000005

   1. Initial program 93.0%

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

      1. +-commutative 93.0%

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

      2. remove-double-neg 93.0%

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

      3. unsub-neg 93.0%

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

      4. *-commutative 93.0%

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

      5. associate-*l/ 89.6%

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

      6. associate-/l* 94.1%

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

      7. fma-neg 94.1%

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

      8. remove-double-neg 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in a around inf 33.6%

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

Alternative 21: 24.9% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.9%

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

   1. clear-num 80.4%

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

   2. un-div-inv 80.5%

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

4. Applied egg-rr 80.5%

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

5. Taylor expanded in a around 0 79.6%

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

   1. +-commutative 79.6%

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

   2. mul-1-neg 79.6%

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

   3. sub-neg 79.6%

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

7. Simplified 79.6%

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

8. Taylor expanded in z around -inf 22.8%

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

Reproduce

herbie shell --seed 2024137 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))