Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A

Percentage Accurate: 84.7% → 95.3%

Time: 13.7s

Alternatives: 11

Speedup: 0.7×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y \cdot z}{t - a \cdot z} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return (x - (y * z)) / (t - (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 - (a * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y \cdot z}{t - a \cdot z} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return (x - (y * z)) / (t - (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 - (a * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.3% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ t_2 := {\left(\frac{\sqrt[3]{x}}{\sqrt[3]{t_1}}\right)}^{3} - y \cdot \frac{z}{t_1}\\ t_3 := \frac{x - y \cdot z}{t_1}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-320}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;\frac{y}{a} + \left(\frac{x}{a} - y \cdot \left(t \cdot {a}^{-2}\right)\right) \cdot \frac{-1}{z}\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* z a)))
        (t_2 (- (pow (/ (cbrt x) (cbrt t_1)) 3.0) (* y (/ z t_1))))
        (t_3 (/ (- x (* y z)) t_1)))
   (if (<= t_3 (- INFINITY))
     t_2
     (if (<= t_3 -5e-320)
       t_3
       (if (<= t_3 0.0)
         (+ (/ y a) (* (- (/ x a) (* y (* t (pow a -2.0)))) (/ -1.0 z)))
         (if (<= t_3 INFINITY) t_2 (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = pow((cbrt(x) / cbrt(t_1)), 3.0) - (y * (z / t_1));
	double t_3 = (x - (y * z)) / t_1;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_3 <= -5e-320) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = (y / a) + (((x / a) - (y * (t * pow(a, -2.0)))) * (-1.0 / z));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = Math.pow((Math.cbrt(x) / Math.cbrt(t_1)), 3.0) - (y * (z / t_1));
	double t_3 = (x - (y * z)) / t_1;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_3 <= -5e-320) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = (y / a) + (((x / a) - (y * (t * Math.pow(a, -2.0)))) * (-1.0 / z));
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(z * a))
	t_2 = Float64((Float64(cbrt(x) / cbrt(t_1)) ^ 3.0) - Float64(y * Float64(z / t_1)))
	t_3 = Float64(Float64(x - Float64(y * z)) / t_1)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_3 <= -5e-320)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(y / a) + Float64(Float64(Float64(x / a) - Float64(y * Float64(t * (a ^ -2.0)))) * Float64(-1.0 / z)));
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Power[N[(N[Power[x, 1/3], $MachinePrecision] / N[Power[t$95$1, 1/3], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision] - N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$2, If[LessEqual[t$95$3, -5e-320], t$95$3, If[LessEqual[t$95$3, 0.0], N[(N[(y / a), $MachinePrecision] + N[(N[(N[(x / a), $MachinePrecision] - N[(y * N[(t * N[Power[a, -2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$2, N[(y / a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -inf.0 or 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 89.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 89.6%

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

   3. Simplified 89.6%

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

      1. div-sub 88.9%

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

      2. sub-neg 88.9%

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

      3. add-cube-cbrt 88.1%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{t - z \cdot a} + \left(-\frac{y \cdot z}{t - z \cdot a}\right) \]

      4. add-cube-cbrt 88.0%

         \[\leadsto \frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}{\color{blue}{\left(\sqrt[3]{t - z \cdot a} \cdot \sqrt[3]{t - z \cdot a}\right) \cdot \sqrt[3]{t - z \cdot a}}} + \left(-\frac{y \cdot z}{t - z \cdot a}\right) \]

      5. times-frac 88.0%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{t - z \cdot a} \cdot \sqrt[3]{t - z \cdot a}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{t - z \cdot a}}} + \left(-\frac{y \cdot z}{t - z \cdot a}\right) \]

      6. fma-def 88.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{t - z \cdot a} \cdot \sqrt[3]{t - z \cdot a}}, \frac{\sqrt[3]{x}}{\sqrt[3]{t - z \cdot a}}, -\frac{y \cdot z}{t - z \cdot a}\right)} \]

   5. Applied egg-rr 97.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{{\left(\sqrt[3]{x}\right)}^{2}}{{\left(\sqrt[3]{\mathsf{fma}\left(a, -z, t\right)}\right)}^{2}}, \frac{\sqrt[3]{x}}{\sqrt[3]{\mathsf{fma}\left(a, -z, t\right)}}, -\frac{y}{\frac{\mathsf{fma}\left(a, -z, t\right)}{z}}\right)} \]
   6. Step-by-step derivation

      1. fma-neg 96.7%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{{\left(\sqrt[3]{\mathsf{fma}\left(a, -z, t\right)}\right)}^{2}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{\mathsf{fma}\left(a, -z, t\right)}} - \frac{y}{\frac{\mathsf{fma}\left(a, -z, t\right)}{z}}} \]

      2. *-commutative 96.7%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x}}{\sqrt[3]{\mathsf{fma}\left(a, -z, t\right)}} \cdot \frac{{\left(\sqrt[3]{x}\right)}^{2}}{{\left(\sqrt[3]{\mathsf{fma}\left(a, -z, t\right)}\right)}^{2}}} - \frac{y}{\frac{\mathsf{fma}\left(a, -z, t\right)}{z}} \]

   7. Simplified 96.7%

      \[\leadsto \color{blue}{{\left(\frac{\sqrt[3]{x}}{\sqrt[3]{t - z \cdot a}}\right)}^{3} - y \cdot \frac{z}{t - z \cdot a}} \]

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -4.99994e-320

   1. Initial program 99.6%

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

   if -4.99994e-320 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 48.0%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 48.0%

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

   3. Simplified 48.0%

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

   4. Taylor expanded in z around inf 43.1%

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

      1. +-commutative 43.1%

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

      2. associate--l+ 43.1%

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

      3. associate-/r* 79.4%

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

      4. associate-*r/ 79.4%

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

      5. associate-/r* 79.4%

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

      6. associate-*r/ 79.4%

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

      7. div-sub 79.4%

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

      8. distribute-lft-out-- 79.4%

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

      9. associate-*r/ 79.4%

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

      10. mul-1-neg 79.4%

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

      11. unsub-neg 79.4%

          \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

   6. Simplified 79.4%

      \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{t}{{a}^{2}} \cdot y}{z}} \]
   7. Step-by-step derivation

      1. div-inv 79.6%

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

      2. *-commutative 79.6%

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

      3. div-inv 79.6%

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

      4. pow-flip 79.6%

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

      5. metadata-eval 79.6%

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

   8. Applied egg-rr 79.6%

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

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

   1. Initial program 0.0%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 100.0%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -\infty:\\ \;\;\;\;{\left(\frac{\sqrt[3]{x}}{\sqrt[3]{t - z \cdot a}}\right)}^{3} - y \cdot \frac{z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -5 \cdot 10^{-320}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{y}{a} + \left(\frac{x}{a} - y \cdot \left(t \cdot {a}^{-2}\right)\right) \cdot \frac{-1}{z}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;{\left(\frac{\sqrt[3]{x}}{\sqrt[3]{t - z \cdot a}}\right)}^{3} - y \cdot \frac{z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 2: 94.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ t_2 := \frac{x}{t_1}\\ t_3 := \frac{x - y \cdot z}{t_1}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_2 - \frac{z}{\frac{t_1}{y}}\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-320}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;\frac{y}{a} + \left(\frac{x}{a} - y \cdot \left(t \cdot {a}^{-2}\right)\right) \cdot \frac{-1}{z}\\ \mathbf{elif}\;t_3 \leq 10^{+279}:\\ \;\;\;\;t_2 - \frac{y \cdot z}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{t}{z} - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* z a))) (t_2 (/ x t_1)) (t_3 (/ (- x (* y z)) t_1)))
   (if (<= t_3 (- INFINITY))
     (- t_2 (/ z (/ t_1 y)))
     (if (<= t_3 -5e-320)
       t_3
       (if (<= t_3 0.0)
         (+ (/ y a) (* (- (/ x a) (* y (* t (pow a -2.0)))) (/ -1.0 z)))
         (if (<= t_3 1e+279)
           (- t_2 (/ (* y z) t_1))
           (/ (- y) (- (/ t z) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = x / t_1;
	double t_3 = (x - (y * z)) / t_1;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_2 - (z / (t_1 / y));
	} else if (t_3 <= -5e-320) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = (y / a) + (((x / a) - (y * (t * pow(a, -2.0)))) * (-1.0 / z));
	} else if (t_3 <= 1e+279) {
		tmp = t_2 - ((y * z) / t_1);
	} else {
		tmp = -y / ((t / z) - a);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = x / t_1;
	double t_3 = (x - (y * z)) / t_1;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2 - (z / (t_1 / y));
	} else if (t_3 <= -5e-320) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = (y / a) + (((x / a) - (y * (t * Math.pow(a, -2.0)))) * (-1.0 / z));
	} else if (t_3 <= 1e+279) {
		tmp = t_2 - ((y * z) / t_1);
	} else {
		tmp = -y / ((t / z) - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (z * a)
	t_2 = x / t_1
	t_3 = (x - (y * z)) / t_1
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_2 - (z / (t_1 / y))
	elif t_3 <= -5e-320:
		tmp = t_3
	elif t_3 <= 0.0:
		tmp = (y / a) + (((x / a) - (y * (t * math.pow(a, -2.0)))) * (-1.0 / z))
	elif t_3 <= 1e+279:
		tmp = t_2 - ((y * z) / t_1)
	else:
		tmp = -y / ((t / z) - a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(z * a))
	t_2 = Float64(x / t_1)
	t_3 = Float64(Float64(x - Float64(y * z)) / t_1)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(t_2 - Float64(z / Float64(t_1 / y)));
	elseif (t_3 <= -5e-320)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(y / a) + Float64(Float64(Float64(x / a) - Float64(y * Float64(t * (a ^ -2.0)))) * Float64(-1.0 / z)));
	elseif (t_3 <= 1e+279)
		tmp = Float64(t_2 - Float64(Float64(y * z) / t_1));
	else
		tmp = Float64(Float64(-y) / Float64(Float64(t / z) - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (z * a);
	t_2 = x / t_1;
	t_3 = (x - (y * z)) / t_1;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_2 - (z / (t_1 / y));
	elseif (t_3 <= -5e-320)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = (y / a) + (((x / a) - (y * (t * (a ^ -2.0)))) * (-1.0 / z));
	elseif (t_3 <= 1e+279)
		tmp = t_2 - ((y * z) / t_1);
	else
		tmp = -y / ((t / z) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(t$95$2 - N[(z / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -5e-320], t$95$3, If[LessEqual[t$95$3, 0.0], N[(N[(y / a), $MachinePrecision] + N[(N[(N[(x / a), $MachinePrecision] - N[(y * N[(t * N[Power[a, -2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 1e+279], N[(t$95$2 - N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[((-y) / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 76.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 76.7%

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

   3. Simplified 76.7%

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

   4. Taylor expanded in x around 0 72.5%

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

      1. clear-num 72.5%

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

      2. inv-pow 72.5%

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

      3. *-commutative 72.5%

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

   6. Applied egg-rr 72.5%

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

      1. unpow-1 72.5%

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

   8. Simplified 72.5%

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

   9. Taylor expanded in y around 0 72.5%

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

       1. +-commutative 72.5%

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

       2. *-commutative 72.5%

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

       3. mul-1-neg 72.5%

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

       4. unsub-neg 72.5%

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

       5. *-commutative 72.5%

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

       6. *-commutative 72.5%

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

       7. *-commutative 72.5%

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

       8. associate-/l* 95.7%

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

       9. *-commutative 95.7%

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

   11. Simplified 95.7%

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

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -4.99994e-320

   1. Initial program 99.6%

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

   if -4.99994e-320 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 48.0%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 48.0%

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

   3. Simplified 48.0%

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

   4. Taylor expanded in z around inf 43.1%

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

      1. +-commutative 43.1%

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

      2. associate--l+ 43.1%

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

      3. associate-/r* 79.4%

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

      4. associate-*r/ 79.4%

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

      5. associate-/r* 79.4%

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

      6. associate-*r/ 79.4%

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

      7. div-sub 79.4%

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

      8. distribute-lft-out-- 79.4%

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

      9. associate-*r/ 79.4%

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

      10. mul-1-neg 79.4%

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

      11. unsub-neg 79.4%

          \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

   6. Simplified 79.4%

      \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{t}{{a}^{2}} \cdot y}{z}} \]
   7. Step-by-step derivation

      1. div-inv 79.6%

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

      2. *-commutative 79.6%

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

      3. div-inv 79.6%

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

      4. pow-flip 79.6%

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

      5. metadata-eval 79.6%

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

   8. Applied egg-rr 79.6%

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

   if 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 1.00000000000000006e279

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 99.8%

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

   if 1.00000000000000006e279 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 36.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 36.6%

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

   3. Simplified 36.6%

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

   4. Taylor expanded in x around 0 25.2%

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

      1. mul-1-neg 25.2%

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

      2. associate-/l* 48.6%

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

      3. *-commutative 48.6%

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

   6. Simplified 48.6%

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

   7. Taylor expanded in t around 0 88.5%

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

      1. neg-mul-1 88.5%

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

      2. +-commutative 88.5%

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

      3. unsub-neg 88.5%

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

   9. Simplified 88.5%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -\infty:\\ \;\;\;\;\frac{x}{t - z \cdot a} - \frac{z}{\frac{t - z \cdot a}{y}}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -5 \cdot 10^{-320}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{y}{a} + \left(\frac{x}{a} - y \cdot \left(t \cdot {a}^{-2}\right)\right) \cdot \frac{-1}{z}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 10^{+279}:\\ \;\;\;\;\frac{x}{t - z \cdot a} - \frac{y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{t}{z} - a}\\ \end{array} \]

Alternative 3: 94.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ t_2 := \frac{x}{t_1}\\ t_3 := \frac{x - y \cdot z}{t_1}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_2 - \frac{z}{\frac{t_1}{y}}\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-320}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;\frac{y}{a} + \frac{y \cdot \frac{t}{{a}^{2}} - \frac{x}{a}}{z}\\ \mathbf{elif}\;t_3 \leq 10^{+279}:\\ \;\;\;\;t_2 - \frac{y \cdot z}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{t}{z} - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* z a))) (t_2 (/ x t_1)) (t_3 (/ (- x (* y z)) t_1)))
   (if (<= t_3 (- INFINITY))
     (- t_2 (/ z (/ t_1 y)))
     (if (<= t_3 -5e-320)
       t_3
       (if (<= t_3 0.0)
         (+ (/ y a) (/ (- (* y (/ t (pow a 2.0))) (/ x a)) z))
         (if (<= t_3 1e+279)
           (- t_2 (/ (* y z) t_1))
           (/ (- y) (- (/ t z) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = x / t_1;
	double t_3 = (x - (y * z)) / t_1;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_2 - (z / (t_1 / y));
	} else if (t_3 <= -5e-320) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = (y / a) + (((y * (t / pow(a, 2.0))) - (x / a)) / z);
	} else if (t_3 <= 1e+279) {
		tmp = t_2 - ((y * z) / t_1);
	} else {
		tmp = -y / ((t / z) - a);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = x / t_1;
	double t_3 = (x - (y * z)) / t_1;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2 - (z / (t_1 / y));
	} else if (t_3 <= -5e-320) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = (y / a) + (((y * (t / Math.pow(a, 2.0))) - (x / a)) / z);
	} else if (t_3 <= 1e+279) {
		tmp = t_2 - ((y * z) / t_1);
	} else {
		tmp = -y / ((t / z) - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (z * a)
	t_2 = x / t_1
	t_3 = (x - (y * z)) / t_1
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_2 - (z / (t_1 / y))
	elif t_3 <= -5e-320:
		tmp = t_3
	elif t_3 <= 0.0:
		tmp = (y / a) + (((y * (t / math.pow(a, 2.0))) - (x / a)) / z)
	elif t_3 <= 1e+279:
		tmp = t_2 - ((y * z) / t_1)
	else:
		tmp = -y / ((t / z) - a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(z * a))
	t_2 = Float64(x / t_1)
	t_3 = Float64(Float64(x - Float64(y * z)) / t_1)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(t_2 - Float64(z / Float64(t_1 / y)));
	elseif (t_3 <= -5e-320)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(y / a) + Float64(Float64(Float64(y * Float64(t / (a ^ 2.0))) - Float64(x / a)) / z));
	elseif (t_3 <= 1e+279)
		tmp = Float64(t_2 - Float64(Float64(y * z) / t_1));
	else
		tmp = Float64(Float64(-y) / Float64(Float64(t / z) - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (z * a);
	t_2 = x / t_1;
	t_3 = (x - (y * z)) / t_1;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_2 - (z / (t_1 / y));
	elseif (t_3 <= -5e-320)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = (y / a) + (((y * (t / (a ^ 2.0))) - (x / a)) / z);
	elseif (t_3 <= 1e+279)
		tmp = t_2 - ((y * z) / t_1);
	else
		tmp = -y / ((t / z) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(t$95$2 - N[(z / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -5e-320], t$95$3, If[LessEqual[t$95$3, 0.0], N[(N[(y / a), $MachinePrecision] + N[(N[(N[(y * N[(t / N[Power[a, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 1e+279], N[(t$95$2 - N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[((-y) / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 76.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 76.7%

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

   3. Simplified 76.7%

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

   4. Taylor expanded in x around 0 72.5%

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

      1. clear-num 72.5%

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

      2. inv-pow 72.5%

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

      3. *-commutative 72.5%

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

   6. Applied egg-rr 72.5%

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

      1. unpow-1 72.5%

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

   8. Simplified 72.5%

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

   9. Taylor expanded in y around 0 72.5%

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

       1. +-commutative 72.5%

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

       2. *-commutative 72.5%

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

       3. mul-1-neg 72.5%

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

       4. unsub-neg 72.5%

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

       5. *-commutative 72.5%

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

       6. *-commutative 72.5%

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

       7. *-commutative 72.5%

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

       8. associate-/l* 95.7%

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

       9. *-commutative 95.7%

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

   11. Simplified 95.7%

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

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -4.99994e-320

   1. Initial program 99.6%

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

   if -4.99994e-320 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 48.0%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 48.0%

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

   3. Simplified 48.0%

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

   4. Taylor expanded in z around inf 43.1%

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

      1. +-commutative 43.1%

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

      2. associate--l+ 43.1%

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

      3. associate-/r* 79.4%

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

      4. associate-*r/ 79.4%

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

      5. associate-/r* 79.4%

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

      6. associate-*r/ 79.4%

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

      7. div-sub 79.4%

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

      8. distribute-lft-out-- 79.4%

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

      9. associate-*r/ 79.4%

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

      10. mul-1-neg 79.4%

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

      11. unsub-neg 79.4%

          \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

   6. Simplified 79.4%

      \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{t}{{a}^{2}} \cdot y}{z}} \]

   if 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 1.00000000000000006e279

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 99.8%

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

   if 1.00000000000000006e279 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 36.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 36.6%

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

   3. Simplified 36.6%

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

   4. Taylor expanded in x around 0 25.2%

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

      1. mul-1-neg 25.2%

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

      2. associate-/l* 48.6%

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

      3. *-commutative 48.6%

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

   6. Simplified 48.6%

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

   7. Taylor expanded in t around 0 88.5%

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

      1. neg-mul-1 88.5%

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

      2. +-commutative 88.5%

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

      3. unsub-neg 88.5%

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

   9. Simplified 88.5%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -\infty:\\ \;\;\;\;\frac{x}{t - z \cdot a} - \frac{z}{\frac{t - z \cdot a}{y}}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -5 \cdot 10^{-320}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{y}{a} + \frac{y \cdot \frac{t}{{a}^{2}} - \frac{x}{a}}{z}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 10^{+279}:\\ \;\;\;\;\frac{x}{t - z \cdot a} - \frac{y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{t}{z} - a}\\ \end{array} \]

Alternative 4: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t}\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{+67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-96}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) t)) (t_2 (/ (- y (/ x z)) a)))
   (if (<= z -1.95e+67)
     t_2
     (if (<= z -9.2e-37)
       t_1
       (if (<= z -5.5e-87)
         t_2
         (if (<= z 3.3e-96)
           (/ x (- t (* z a)))
           (if (<= z 2.4e+19) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / t;
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.95e+67) {
		tmp = t_2;
	} else if (z <= -9.2e-37) {
		tmp = t_1;
	} else if (z <= -5.5e-87) {
		tmp = t_2;
	} else if (z <= 3.3e-96) {
		tmp = x / (t - (z * a));
	} else if (z <= 2.4e+19) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - (y * z)) / t
    t_2 = (y - (x / z)) / a
    if (z <= (-1.95d+67)) then
        tmp = t_2
    else if (z <= (-9.2d-37)) then
        tmp = t_1
    else if (z <= (-5.5d-87)) then
        tmp = t_2
    else if (z <= 3.3d-96) then
        tmp = x / (t - (z * a))
    else if (z <= 2.4d+19) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / t;
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.95e+67) {
		tmp = t_2;
	} else if (z <= -9.2e-37) {
		tmp = t_1;
	} else if (z <= -5.5e-87) {
		tmp = t_2;
	} else if (z <= 3.3e-96) {
		tmp = x / (t - (z * a));
	} else if (z <= 2.4e+19) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y * z)) / t
	t_2 = (y - (x / z)) / a
	tmp = 0
	if z <= -1.95e+67:
		tmp = t_2
	elif z <= -9.2e-37:
		tmp = t_1
	elif z <= -5.5e-87:
		tmp = t_2
	elif z <= 3.3e-96:
		tmp = x / (t - (z * a))
	elif z <= 2.4e+19:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(y * z)) / t)
	t_2 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -1.95e+67)
		tmp = t_2;
	elseif (z <= -9.2e-37)
		tmp = t_1;
	elseif (z <= -5.5e-87)
		tmp = t_2;
	elseif (z <= 3.3e-96)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 2.4e+19)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (y * z)) / t;
	t_2 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -1.95e+67)
		tmp = t_2;
	elseif (z <= -9.2e-37)
		tmp = t_1;
	elseif (z <= -5.5e-87)
		tmp = t_2;
	elseif (z <= 3.3e-96)
		tmp = x / (t - (z * a));
	elseif (z <= 2.4e+19)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -1.95e+67], t$95$2, If[LessEqual[z, -9.2e-37], t$95$1, If[LessEqual[z, -5.5e-87], t$95$2, If[LessEqual[z, 3.3e-96], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+19], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.95000000000000003e67 or -9.1999999999999999e-37 < z < -5.5000000000000004e-87 or 2.4e19 < z

   1. Initial program 68.1%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 68.1%

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

   3. Simplified 68.1%

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

   4. Taylor expanded in z around inf 60.2%

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

      1. +-commutative 60.2%

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

      2. associate--l+ 60.2%

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

      3. associate-/r* 64.2%

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

      4. associate-*r/ 64.2%

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

      5. associate-/r* 62.6%

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

      6. associate-*r/ 62.6%

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

      7. div-sub 62.6%

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

      8. distribute-lft-out-- 62.6%

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

      9. associate-*r/ 62.6%

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

      10. mul-1-neg 62.6%

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

      11. unsub-neg 62.6%

          \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

   6. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{t}{{a}^{2}} \cdot y}{z}} \]

   7. Taylor expanded in a around inf 79.4%

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

   if -1.95000000000000003e67 < z < -9.1999999999999999e-37 or 3.2999999999999999e-96 < z < 2.4e19

   1. Initial program 97.5%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in t around inf 75.1%

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

   if -5.5000000000000004e-87 < z < 3.2999999999999999e-96

   1. Initial program 99.9%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 81.1%

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

      1. *-commutative 81.1%

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

   6. Simplified 81.1%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+67}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-37}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-87}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-96}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+19}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 5: 67.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+90}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+18}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 2.92 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))))
   (if (<= z -9.5e+90)
     (/ y a)
     (if (<= z 6.8e-98)
       t_1
       (if (<= z 3.7e+18)
         (/ (- x (* y z)) t)
         (if (<= z 2.92e+93) t_1 (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double tmp;
	if (z <= -9.5e+90) {
		tmp = y / a;
	} else if (z <= 6.8e-98) {
		tmp = t_1;
	} else if (z <= 3.7e+18) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 2.92e+93) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (t - (z * a))
    if (z <= (-9.5d+90)) then
        tmp = y / a
    else if (z <= 6.8d-98) then
        tmp = t_1
    else if (z <= 3.7d+18) then
        tmp = (x - (y * z)) / t
    else if (z <= 2.92d+93) then
        tmp = t_1
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double tmp;
	if (z <= -9.5e+90) {
		tmp = y / a;
	} else if (z <= 6.8e-98) {
		tmp = t_1;
	} else if (z <= 3.7e+18) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 2.92e+93) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	tmp = 0
	if z <= -9.5e+90:
		tmp = y / a
	elif z <= 6.8e-98:
		tmp = t_1
	elif z <= 3.7e+18:
		tmp = (x - (y * z)) / t
	elif z <= 2.92e+93:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (z <= -9.5e+90)
		tmp = Float64(y / a);
	elseif (z <= 6.8e-98)
		tmp = t_1;
	elseif (z <= 3.7e+18)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (z <= 2.92e+93)
		tmp = t_1;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t - (z * a));
	tmp = 0.0;
	if (z <= -9.5e+90)
		tmp = y / a;
	elseif (z <= 6.8e-98)
		tmp = t_1;
	elseif (z <= 3.7e+18)
		tmp = (x - (y * z)) / t;
	elseif (z <= 2.92e+93)
		tmp = t_1;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e+90], N[(y / a), $MachinePrecision], If[LessEqual[z, 6.8e-98], t$95$1, If[LessEqual[z, 3.7e+18], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 2.92e+93], t$95$1, N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.4999999999999994e90 or 2.9200000000000002e93 < z

   1. Initial program 63.1%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 63.1%

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

   3. Simplified 63.1%

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

   4. Taylor expanded in z around inf 71.4%

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

   if -9.4999999999999994e90 < z < 6.8000000000000003e-98 or 3.7e18 < z < 2.9200000000000002e93

   1. Initial program 96.4%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in x around inf 70.4%

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

      1. *-commutative 70.4%

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

   6. Simplified 70.4%

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

   if 6.8000000000000003e-98 < z < 3.7e18

   1. Initial program 99.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around inf 84.7%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+90}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+18}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 2.92 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 6: 91.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+94} \lor \neg \left(z \leq 2.92 \cdot 10^{+93}\right):\\ \;\;\;\;\frac{-y}{\frac{t}{z} - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.6e+94) (not (<= z 2.92e+93)))
   (/ (- y) (- (/ t z) a))
   (/ (- x (* y z)) (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.6e+94) || !(z <= 2.92e+93)) {
		tmp = -y / ((t / z) - a);
	} else {
		tmp = (x - (y * z)) / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6.6d+94)) .or. (.not. (z <= 2.92d+93))) then
        tmp = -y / ((t / z) - a)
    else
        tmp = (x - (y * z)) / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.6e+94) || !(z <= 2.92e+93)) {
		tmp = -y / ((t / z) - a);
	} else {
		tmp = (x - (y * z)) / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.6e+94) or not (z <= 2.92e+93):
		tmp = -y / ((t / z) - a)
	else:
		tmp = (x - (y * z)) / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.6e+94) || !(z <= 2.92e+93))
		tmp = Float64(Float64(-y) / Float64(Float64(t / z) - a));
	else
		tmp = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.6e+94) || ~((z <= 2.92e+93)))
		tmp = -y / ((t / z) - a);
	else
		tmp = (x - (y * z)) / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.6e+94], N[Not[LessEqual[z, 2.92e+93]], $MachinePrecision]], N[((-y) / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.6e94 or 2.9200000000000002e93 < z

   1. Initial program 63.1%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 63.1%

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

   3. Simplified 63.1%

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

   4. Taylor expanded in x around 0 54.7%

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

      1. mul-1-neg 54.7%

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

      2. associate-/l* 66.1%

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

      3. *-commutative 66.1%

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

   6. Simplified 66.1%

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

   7. Taylor expanded in t around 0 85.3%

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

      1. neg-mul-1 85.3%

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

      2. +-commutative 85.3%

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

      3. unsub-neg 85.3%

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

   9. Simplified 85.3%

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

   if -6.6e94 < z < 2.9200000000000002e93

   1. Initial program 96.9%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+94} \lor \neg \left(z \leq 2.92 \cdot 10^{+93}\right):\\ \;\;\;\;\frac{-y}{\frac{t}{z} - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \end{array} \]

Alternative 7: 74.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-y}{\frac{t}{z} - a}\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-96}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+24}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y) (- (/ t z) a))))
   (if (<= z -2.35e-45)
     t_1
     (if (<= z 4.5e-96)
       (/ x (- t (* z a)))
       (if (<= z 8.8e+24) (/ (- x (* y z)) t) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -y / ((t / z) - a);
	double tmp;
	if (z <= -2.35e-45) {
		tmp = t_1;
	} else if (z <= 4.5e-96) {
		tmp = x / (t - (z * a));
	} else if (z <= 8.8e+24) {
		tmp = (x - (y * z)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -y / ((t / z) - a)
    if (z <= (-2.35d-45)) then
        tmp = t_1
    else if (z <= 4.5d-96) then
        tmp = x / (t - (z * a))
    else if (z <= 8.8d+24) then
        tmp = (x - (y * z)) / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -y / ((t / z) - a);
	double tmp;
	if (z <= -2.35e-45) {
		tmp = t_1;
	} else if (z <= 4.5e-96) {
		tmp = x / (t - (z * a));
	} else if (z <= 8.8e+24) {
		tmp = (x - (y * z)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -y / ((t / z) - a)
	tmp = 0
	if z <= -2.35e-45:
		tmp = t_1
	elif z <= 4.5e-96:
		tmp = x / (t - (z * a))
	elif z <= 8.8e+24:
		tmp = (x - (y * z)) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-y) / Float64(Float64(t / z) - a))
	tmp = 0.0
	if (z <= -2.35e-45)
		tmp = t_1;
	elseif (z <= 4.5e-96)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 8.8e+24)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -y / ((t / z) - a);
	tmp = 0.0;
	if (z <= -2.35e-45)
		tmp = t_1;
	elseif (z <= 4.5e-96)
		tmp = x / (t - (z * a));
	elseif (z <= 8.8e+24)
		tmp = (x - (y * z)) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-y) / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.35e-45], t$95$1, If[LessEqual[z, 4.5e-96], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e+24], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3499999999999999e-45 or 8.80000000000000007e24 < z

   1. Initial program 70.4%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 70.4%

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

   3. Simplified 70.4%

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

   4. Taylor expanded in x around 0 54.1%

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

      1. mul-1-neg 54.1%

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

      2. associate-/l* 64.2%

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

      3. *-commutative 64.2%

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

   6. Simplified 64.2%

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

   7. Taylor expanded in t around 0 78.5%

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

      1. neg-mul-1 78.5%

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

      2. +-commutative 78.5%

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

      3. unsub-neg 78.5%

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

   9. Simplified 78.5%

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

   if -2.3499999999999999e-45 < z < 4.5e-96

   1. Initial program 99.9%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 79.5%

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

      1. *-commutative 79.5%

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

   6. Simplified 79.5%

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

   if 4.5e-96 < z < 8.80000000000000007e24

   1. Initial program 99.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around inf 81.8%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-45}:\\ \;\;\;\;\frac{-y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-96}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+24}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{t}{z} - a}\\ \end{array} \]

Alternative 8: 67.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+92} \lor \neg \left(z \leq 2.92 \cdot 10^{+93}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.15e+92) (not (<= z 2.92e+93))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e+92) || !(z <= 2.92e+93)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.15d+92)) .or. (.not. (z <= 2.92d+93))) then
        tmp = y / a
    else
        tmp = x / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e+92) || !(z <= 2.92e+93)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.15e+92) or not (z <= 2.92e+93):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.15e+92) || !(z <= 2.92e+93))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.15e+92) || ~((z <= 2.92e+93)))
		tmp = y / a;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.15e+92], N[Not[LessEqual[z, 2.92e+93]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.14999999999999999e92 or 2.9200000000000002e93 < z

   1. Initial program 63.1%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 63.1%

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

   3. Simplified 63.1%

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

   4. Taylor expanded in z around inf 71.4%

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

   if -1.14999999999999999e92 < z < 2.9200000000000002e93

   1. Initial program 96.9%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in x around inf 68.5%

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

      1. *-commutative 68.5%

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

   6. Simplified 68.5%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+92} \lor \neg \left(z \leq 2.92 \cdot 10^{+93}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]

Alternative 9: 54.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{-58}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-154}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.15e-58)
   (/ y a)
   (if (<= z -1.45e-154)
     (/ (- x) (* z a))
     (if (<= z 1.4e+24) (/ x t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.15e-58) {
		tmp = y / a;
	} else if (z <= -1.45e-154) {
		tmp = -x / (z * a);
	} else if (z <= 1.4e+24) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.15d-58)) then
        tmp = y / a
    else if (z <= (-1.45d-154)) then
        tmp = -x / (z * a)
    else if (z <= 1.4d+24) then
        tmp = x / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.15e-58) {
		tmp = y / a;
	} else if (z <= -1.45e-154) {
		tmp = -x / (z * a);
	} else if (z <= 1.4e+24) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.15e-58:
		tmp = y / a
	elif z <= -1.45e-154:
		tmp = -x / (z * a)
	elif z <= 1.4e+24:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.15e-58)
		tmp = Float64(y / a);
	elseif (z <= -1.45e-154)
		tmp = Float64(Float64(-x) / Float64(z * a));
	elseif (z <= 1.4e+24)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.15e-58)
		tmp = y / a;
	elseif (z <= -1.45e-154)
		tmp = -x / (z * a);
	elseif (z <= 1.4e+24)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.15e-58], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.45e-154], N[((-x) / N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+24], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.14999999999999999e-58 or 1.4000000000000001e24 < z

   1. Initial program 70.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 70.6%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in z around inf 59.7%

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

   if -3.14999999999999999e-58 < z < -1.45e-154

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 59.3%

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

      1. +-commutative 59.3%

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

      2. associate--l+ 59.3%

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

      3. associate-/r* 59.1%

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

      4. associate-*r/ 59.1%

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

      5. associate-/r* 59.1%

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

      6. associate-*r/ 59.1%

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

      7. div-sub 59.1%

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

      8. distribute-lft-out-- 59.1%

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

      9. associate-*r/ 59.1%

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

      10. mul-1-neg 59.1%

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

      11. unsub-neg 59.1%

          \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

   6. Simplified 59.4%

      \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{t}{{a}^{2}} \cdot y}{z}} \]

   7. Taylor expanded in y around 0 55.2%

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

      1. mul-1-neg 55.2%

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

   9. Simplified 55.2%

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

   if -1.45e-154 < z < 1.4000000000000001e24

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 60.3%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{-58}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-154}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 10: 56.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-30} \lor \neg \left(z \leq 8.5 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.4e-30) (not (<= z 8.5e+26))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.4e-30) || !(z <= 8.5e+26)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.4d-30)) .or. (.not. (z <= 8.5d+26))) then
        tmp = y / a
    else
        tmp = x / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.4e-30) || !(z <= 8.5e+26)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.4e-30) or not (z <= 8.5e+26):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.4e-30) || !(z <= 8.5e+26))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.4e-30) || ~((z <= 8.5e+26)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.4e-30], N[Not[LessEqual[z, 8.5e+26]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4000000000000003e-30 or 8.5e26 < z

   1. Initial program 69.0%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 69.0%

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

   3. Simplified 69.0%

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

   4. Taylor expanded in z around inf 61.3%

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

   if -3.4000000000000003e-30 < z < 8.5e26

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 53.9%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-30} \lor \neg \left(z \leq 8.5 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]

Alternative 11: 34.8% accurate, 3.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x / 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 = x / t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x / t), $MachinePrecision]

Derivation

1. Initial program 84.3%

   \[\frac{x - y \cdot z}{t - a \cdot z} \]
2. Step-by-step derivation

   1. *-commutative 84.3%

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

3. Simplified 84.3%

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

4. Taylor expanded in z around 0 32.4%

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

5. Final simplification 32.4%

   \[\leadsto \frac{x}{t} \]

Developer target: 97.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot z\\ t_2 := \frac{x}{t_1} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{if}\;z < -32113435955957344:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z < 3.5139522372978296 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a z))) (t_2 (- (/ x t_1) (/ y (- (/ t z) a)))))
   (if (< z -32113435955957344.0)
     t_2
     (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 t_1)) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - (a * z)
    t_2 = (x / t_1) - (y / ((t / z) - a))
    if (z < (-32113435955957344.0d0)) then
        tmp = t_2
    else if (z < 3.5139522372978296d-86) then
        tmp = (x - (y * z)) * (1.0d0 / t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a * z)
	t_2 = (x / t_1) - (y / ((t / z) - a))
	tmp = 0
	if z < -32113435955957344.0:
		tmp = t_2
	elif z < 3.5139522372978296e-86:
		tmp = (x - (y * z)) * (1.0 / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a * z))
	t_2 = Float64(Float64(x / t_1) - Float64(y / Float64(Float64(t / z) - a)))
	tmp = 0.0
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = Float64(Float64(x - Float64(y * z)) * Float64(1.0 / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a * z);
	t_2 = (x / t_1) - (y / ((t / z) - a));
	tmp = 0.0;
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = (x - (y * z)) * (1.0 / t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / t$95$1), $MachinePrecision] - N[(y / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -32113435955957344.0], t$95$2, If[Less[z, 3.5139522372978296e-86], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023336 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< z -32113435955957344.0) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

  (/ (- x (* y z)) (- t (* a z))))