Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B

Percentage Accurate: 77.3% → 89.7%

Time: 8.4s

Alternatives: 10

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+28} \lor \neg \left(t \leq 8 \cdot 10^{+93}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{t - a}, x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.3e+28) (not (<= t 8e+93)))
   (+ x (* (/ y t) (- z a)))
   (fma (- z t) (/ y (- t a)) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.3e+28) || !(t <= 8e+93)) {
		tmp = x + ((y / t) * (z - a));
	} else {
		tmp = fma((z - t), (y / (t - a)), (x + y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.3e+28) || !(t <= 8e+93))
		tmp = Float64(x + Float64(Float64(y / t) * Float64(z - a)));
	else
		tmp = fma(Float64(z - t), Float64(y / Float64(t - a)), Float64(x + y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.3e+28], N[Not[LessEqual[t, 8e+93]], $MachinePrecision]], N[(x + N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3000000000000001e28 or 8.00000000000000035e93 < t

   1. Initial program 53.7%

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

   3. Taylor expanded in t around inf 86.5%

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

      1. associate--l+ 86.5%

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

      2. distribute-lft-out-- 86.5%

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

      3. div-sub 86.5%

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

      4. mul-1-neg 86.5%

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

      5. unsub-neg 86.5%

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

      6. *-commutative 86.5%

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

      7. distribute-lft-out-- 86.5%

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

   5. Simplified 86.5%

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

   6. Taylor expanded in a around 0 86.5%

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

      1. mul-1-neg 86.5%

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

      2. sub-neg 86.5%

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

      3. associate--l- 86.5%

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

      4. +-commutative 86.5%

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

      5. associate--l- 86.5%

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

      6. cancel-sign-sub-inv 86.5%

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

      7. metadata-eval 86.5%

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

      8. associate-*r/ 90.2%

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

      9. *-lft-identity 90.2%

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

      10. associate-+r- 90.2%

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

      11. associate-*r/ 86.5%

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

      12. *-commutative 86.5%

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

      13. associate-*r/ 90.3%

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

      14. associate-/l* 93.2%

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

      15. distribute-rgt-out-- 93.2%

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

   8. Simplified 93.2%

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

   if -1.3000000000000001e28 < t < 8.00000000000000035e93

   1. Initial program 93.0%

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

      1. sub-neg 93.0%

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

      2. +-commutative 93.0%

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

      3. distribute-frac-neg 93.0%

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

      4. distribute-rgt-neg-out 93.0%

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

      5. associate-/l* 97.9%

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

      6. fma-define 97.9%

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

      7. distribute-frac-neg 97.9%

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

      8. distribute-neg-frac2 97.9%

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

      9. sub-neg 97.9%

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

      10. distribute-neg-in 97.9%

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

      11. remove-double-neg 97.9%

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

      12. +-commutative 97.9%

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

      13. sub-neg 97.9%

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

   3. Simplified 97.9%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+28} \lor \neg \left(t \leq 8 \cdot 10^{+93}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{t - a}, x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 62.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-87}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-191}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-227}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-276}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.5e-87)
   (+ x y)
   (if (<= a -2.8e-191)
     (* y (/ z (- t a)))
     (if (<= a -1.9e-227)
       x
       (if (<= a -6.6e-276) (* (/ y t) z) (if (<= a 2.1e-65) x (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.5e-87) {
		tmp = x + y;
	} else if (a <= -2.8e-191) {
		tmp = y * (z / (t - a));
	} else if (a <= -1.9e-227) {
		tmp = x;
	} else if (a <= -6.6e-276) {
		tmp = (y / t) * z;
	} else if (a <= 2.1e-65) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	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 <= (-8.5d-87)) then
        tmp = x + y
    else if (a <= (-2.8d-191)) then
        tmp = y * (z / (t - a))
    else if (a <= (-1.9d-227)) then
        tmp = x
    else if (a <= (-6.6d-276)) then
        tmp = (y / t) * z
    else if (a <= 2.1d-65) then
        tmp = x
    else
        tmp = x + y
    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 <= -8.5e-87) {
		tmp = x + y;
	} else if (a <= -2.8e-191) {
		tmp = y * (z / (t - a));
	} else if (a <= -1.9e-227) {
		tmp = x;
	} else if (a <= -6.6e-276) {
		tmp = (y / t) * z;
	} else if (a <= 2.1e-65) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.5e-87:
		tmp = x + y
	elif a <= -2.8e-191:
		tmp = y * (z / (t - a))
	elif a <= -1.9e-227:
		tmp = x
	elif a <= -6.6e-276:
		tmp = (y / t) * z
	elif a <= 2.1e-65:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.5e-87)
		tmp = Float64(x + y);
	elseif (a <= -2.8e-191)
		tmp = Float64(y * Float64(z / Float64(t - a)));
	elseif (a <= -1.9e-227)
		tmp = x;
	elseif (a <= -6.6e-276)
		tmp = Float64(Float64(y / t) * z);
	elseif (a <= 2.1e-65)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.5e-87)
		tmp = x + y;
	elseif (a <= -2.8e-191)
		tmp = y * (z / (t - a));
	elseif (a <= -1.9e-227)
		tmp = x;
	elseif (a <= -6.6e-276)
		tmp = (y / t) * z;
	elseif (a <= 2.1e-65)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.5e-87], N[(x + y), $MachinePrecision], If[LessEqual[a, -2.8e-191], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.9e-227], x, If[LessEqual[a, -6.6e-276], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[a, 2.1e-65], x, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.5000000000000001e-87 or 2.10000000000000003e-65 < a

   1. Initial program 82.7%

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

   3. Taylor expanded in a around inf 72.1%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 72.1%

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

   5. Simplified 72.1%

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

   if -8.5000000000000001e-87 < a < -2.80000000000000012e-191

   1. Initial program 69.7%

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

      1. sub-neg 69.7%

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

      2. +-commutative 69.7%

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

      3. distribute-frac-neg 69.7%

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

      4. distribute-rgt-neg-out 69.7%

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

      5. associate-/l* 73.4%

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

      6. fma-define 73.4%

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

      7. distribute-frac-neg 73.4%

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

      8. distribute-neg-frac2 73.4%

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

      9. sub-neg 73.4%

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

      10. distribute-neg-in 73.4%

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

      11. remove-double-neg 73.4%

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

      12. +-commutative 73.4%

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

      13. sub-neg 73.4%

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

   3. Simplified 73.4%

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

   5. Taylor expanded in z around inf 65.1%

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

      1. associate-/l* 64.3%

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

   7. Simplified 64.3%

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

   if -2.80000000000000012e-191 < a < -1.90000000000000005e-227 or -6.59999999999999982e-276 < a < 2.10000000000000003e-65

   1. Initial program 74.9%

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

   3. Taylor expanded in x around inf 69.3%

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

   if -1.90000000000000005e-227 < a < -6.59999999999999982e-276

   1. Initial program 48.9%

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

      1. sub-neg 48.9%

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

      2. +-commutative 48.9%

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

      3. distribute-frac-neg 48.9%

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

      4. distribute-rgt-neg-out 48.9%

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

      5. associate-/l* 48.9%

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

      6. fma-define 49.1%

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

      7. distribute-frac-neg 49.1%

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

      8. distribute-neg-frac2 49.1%

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

      9. sub-neg 49.1%

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

      10. distribute-neg-in 49.1%

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

      11. remove-double-neg 49.1%

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

      12. +-commutative 49.1%

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

      13. sub-neg 49.1%

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

   3. Simplified 49.1%

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

   5. Taylor expanded in z around inf 79.0%

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

   6. Taylor expanded in t around inf 79.0%

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

      1. *-commutative 79.0%

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

      2. associate-/l* 79.1%

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

   8. Applied egg-rr 79.1%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-87}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-191}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-227}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-276}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-81}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-191}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-227}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-276}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.8e-81)
   (+ x y)
   (if (<= a -3.9e-191)
     (* z (/ y (- t a)))
     (if (<= a -1e-227)
       x
       (if (<= a -1.6e-276) (* (/ y t) z) (if (<= a 3.4e-65) x (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.8e-81) {
		tmp = x + y;
	} else if (a <= -3.9e-191) {
		tmp = z * (y / (t - a));
	} else if (a <= -1e-227) {
		tmp = x;
	} else if (a <= -1.6e-276) {
		tmp = (y / t) * z;
	} else if (a <= 3.4e-65) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	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 <= (-2.8d-81)) then
        tmp = x + y
    else if (a <= (-3.9d-191)) then
        tmp = z * (y / (t - a))
    else if (a <= (-1d-227)) then
        tmp = x
    else if (a <= (-1.6d-276)) then
        tmp = (y / t) * z
    else if (a <= 3.4d-65) then
        tmp = x
    else
        tmp = x + y
    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 <= -2.8e-81) {
		tmp = x + y;
	} else if (a <= -3.9e-191) {
		tmp = z * (y / (t - a));
	} else if (a <= -1e-227) {
		tmp = x;
	} else if (a <= -1.6e-276) {
		tmp = (y / t) * z;
	} else if (a <= 3.4e-65) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.8e-81:
		tmp = x + y
	elif a <= -3.9e-191:
		tmp = z * (y / (t - a))
	elif a <= -1e-227:
		tmp = x
	elif a <= -1.6e-276:
		tmp = (y / t) * z
	elif a <= 3.4e-65:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.8e-81)
		tmp = Float64(x + y);
	elseif (a <= -3.9e-191)
		tmp = Float64(z * Float64(y / Float64(t - a)));
	elseif (a <= -1e-227)
		tmp = x;
	elseif (a <= -1.6e-276)
		tmp = Float64(Float64(y / t) * z);
	elseif (a <= 3.4e-65)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.8e-81)
		tmp = x + y;
	elseif (a <= -3.9e-191)
		tmp = z * (y / (t - a));
	elseif (a <= -1e-227)
		tmp = x;
	elseif (a <= -1.6e-276)
		tmp = (y / t) * z;
	elseif (a <= 3.4e-65)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.8e-81], N[(x + y), $MachinePrecision], If[LessEqual[a, -3.9e-191], N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1e-227], x, If[LessEqual[a, -1.6e-276], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[a, 3.4e-65], x, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.7999999999999999e-81 or 3.39999999999999987e-65 < a

   1. Initial program 82.7%

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

   3. Taylor expanded in a around inf 72.1%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 72.1%

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

   5. Simplified 72.1%

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

   if -2.7999999999999999e-81 < a < -3.8999999999999999e-191

   1. Initial program 69.7%

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

      1. sub-neg 69.7%

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

      2. +-commutative 69.7%

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

      3. distribute-frac-neg 69.7%

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

      4. distribute-rgt-neg-out 69.7%

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

      5. associate-/l* 73.4%

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

      6. fma-define 73.4%

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

      7. distribute-frac-neg 73.4%

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

      8. distribute-neg-frac2 73.4%

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

      9. sub-neg 73.4%

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

      10. distribute-neg-in 73.4%

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

      11. remove-double-neg 73.4%

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

      12. +-commutative 73.4%

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

      13. sub-neg 73.4%

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

   3. Simplified 73.4%

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

   5. Taylor expanded in z around inf 65.1%

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

      1. *-commutative 65.1%

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

      2. associate-/l* 68.6%

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

   7. Applied egg-rr 68.6%

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

   if -3.8999999999999999e-191 < a < -9.99999999999999945e-228 or -1.59999999999999995e-276 < a < 3.39999999999999987e-65

   1. Initial program 74.9%

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

   3. Taylor expanded in x around inf 69.3%

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

   if -9.99999999999999945e-228 < a < -1.59999999999999995e-276

   1. Initial program 48.9%

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

      1. sub-neg 48.9%

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

      2. +-commutative 48.9%

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

      3. distribute-frac-neg 48.9%

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

      4. distribute-rgt-neg-out 48.9%

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

      5. associate-/l* 48.9%

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

      6. fma-define 49.1%

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

      7. distribute-frac-neg 49.1%

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

      8. distribute-neg-frac2 49.1%

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

      9. sub-neg 49.1%

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

      10. distribute-neg-in 49.1%

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

      11. remove-double-neg 49.1%

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

      12. +-commutative 49.1%

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

      13. sub-neg 49.1%

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

   3. Simplified 49.1%

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

   5. Taylor expanded in z around inf 79.0%

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

   6. Taylor expanded in t around inf 79.0%

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

      1. *-commutative 79.0%

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

      2. associate-/l* 79.1%

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

   8. Applied egg-rr 79.1%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-81}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-191}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-227}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-276}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+29} \lor \neg \left(t \leq 5.6 \cdot 10^{+93}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \frac{y}{a - t} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.4e+29) (not (<= t 5.6e+93)))
   (+ x (* (/ y t) (- z a)))
   (+ (+ x y) (* (/ y (- a t)) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e+29) || !(t <= 5.6e+93)) {
		tmp = x + ((y / t) * (z - a));
	} else {
		tmp = (x + y) + ((y / (a - t)) * (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.4d+29)) .or. (.not. (t <= 5.6d+93))) then
        tmp = x + ((y / t) * (z - a))
    else
        tmp = (x + y) + ((y / (a - t)) * (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e+29) || !(t <= 5.6e+93)) {
		tmp = x + ((y / t) * (z - a));
	} else {
		tmp = (x + y) + ((y / (a - t)) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.4e+29) or not (t <= 5.6e+93):
		tmp = x + ((y / t) * (z - a))
	else:
		tmp = (x + y) + ((y / (a - t)) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.4e+29) || !(t <= 5.6e+93))
		tmp = Float64(x + Float64(Float64(y / t) * Float64(z - a)));
	else
		tmp = Float64(Float64(x + y) + Float64(Float64(y / Float64(a - t)) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.4e+29) || ~((t <= 5.6e+93)))
		tmp = x + ((y / t) * (z - a));
	else
		tmp = (x + y) + ((y / (a - t)) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.4e+29], N[Not[LessEqual[t, 5.6e+93]], $MachinePrecision]], N[(x + N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.4000000000000001e29 or 5.59999999999999978e93 < t

   1. Initial program 53.7%

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

   3. Taylor expanded in t around inf 86.5%

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

      1. associate--l+ 86.5%

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

      2. distribute-lft-out-- 86.5%

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

      3. div-sub 86.5%

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

      4. mul-1-neg 86.5%

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

      5. unsub-neg 86.5%

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

      6. *-commutative 86.5%

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

      7. distribute-lft-out-- 86.5%

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

   5. Simplified 86.5%

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

   6. Taylor expanded in a around 0 86.5%

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

      1. mul-1-neg 86.5%

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

      2. sub-neg 86.5%

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

      3. associate--l- 86.5%

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

      4. +-commutative 86.5%

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

      5. associate--l- 86.5%

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

      6. cancel-sign-sub-inv 86.5%

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

      7. metadata-eval 86.5%

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

      8. associate-*r/ 90.2%

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

      9. *-lft-identity 90.2%

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

      10. associate-+r- 90.2%

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

      11. associate-*r/ 86.5%

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

      12. *-commutative 86.5%

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

      13. associate-*r/ 90.3%

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

      14. associate-/l* 93.2%

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

      15. distribute-rgt-out-- 93.2%

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

   8. Simplified 93.2%

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

   if -2.4000000000000001e29 < t < 5.59999999999999978e93

   1. Initial program 93.0%

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

   3. Taylor expanded in y around 0 93.0%

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

      1. associate-*l/ 97.9%

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

   5. Simplified 97.9%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+29} \lor \neg \left(t \leq 5.6 \cdot 10^{+93}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \frac{y}{a - t} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+30} \lor \neg \left(t \leq 3 \cdot 10^{+90}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + z \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.05e+30) (not (<= t 3e+90)))
   (+ x (* (/ y t) (- z a)))
   (+ (+ x y) (* z (/ y (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e+30) || !(t <= 3e+90)) {
		tmp = x + ((y / t) * (z - a));
	} else {
		tmp = (x + y) + (z * (y / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.05d+30)) .or. (.not. (t <= 3d+90))) then
        tmp = x + ((y / t) * (z - a))
    else
        tmp = (x + y) + (z * (y / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e+30) || !(t <= 3e+90)) {
		tmp = x + ((y / t) * (z - a));
	} else {
		tmp = (x + y) + (z * (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.05e+30) or not (t <= 3e+90):
		tmp = x + ((y / t) * (z - a))
	else:
		tmp = (x + y) + (z * (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.05e+30) || !(t <= 3e+90))
		tmp = Float64(x + Float64(Float64(y / t) * Float64(z - a)));
	else
		tmp = Float64(Float64(x + y) + Float64(z * Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.05e+30) || ~((t <= 3e+90)))
		tmp = x + ((y / t) * (z - a));
	else
		tmp = (x + y) + (z * (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.05e+30], N[Not[LessEqual[t, 3e+90]], $MachinePrecision]], N[(x + N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e30 or 2.99999999999999979e90 < t

   1. Initial program 53.7%

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

   3. Taylor expanded in t around inf 86.5%

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

      1. associate--l+ 86.5%

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

      2. distribute-lft-out-- 86.5%

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

      3. div-sub 86.5%

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

      4. mul-1-neg 86.5%

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

      5. unsub-neg 86.5%

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

      6. *-commutative 86.5%

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

      7. distribute-lft-out-- 86.5%

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

   5. Simplified 86.5%

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

   6. Taylor expanded in a around 0 86.5%

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

      1. mul-1-neg 86.5%

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

      2. sub-neg 86.5%

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

      3. associate--l- 86.5%

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

      4. +-commutative 86.5%

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

      5. associate--l- 86.5%

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

      6. cancel-sign-sub-inv 86.5%

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

      7. metadata-eval 86.5%

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

      8. associate-*r/ 90.2%

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

      9. *-lft-identity 90.2%

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

      10. associate-+r- 90.2%

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

      11. associate-*r/ 86.5%

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

      12. *-commutative 86.5%

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

      13. associate-*r/ 90.3%

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

      14. associate-/l* 93.2%

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

      15. distribute-rgt-out-- 93.2%

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

   8. Simplified 93.2%

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

   if -1.05e30 < t < 2.99999999999999979e90

   1. Initial program 93.0%

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

   3. Taylor expanded in z around inf 91.4%

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

      1. *-commutative 91.4%

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

      2. associate-/l* 96.8%

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

   5. Applied egg-rr 96.8%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+30} \lor \neg \left(t \leq 3 \cdot 10^{+90}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + z \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -33500000000000 \lor \neg \left(a \leq 4.6 \cdot 10^{-38}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -33500000000000.0) (not (<= a 4.6e-38)))
   (+ x y)
   (+ x (* (/ y t) (- z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -33500000000000.0) || !(a <= 4.6e-38)) {
		tmp = x + y;
	} else {
		tmp = x + ((y / 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 ((a <= (-33500000000000.0d0)) .or. (.not. (a <= 4.6d-38))) then
        tmp = x + y
    else
        tmp = x + ((y / 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 ((a <= -33500000000000.0) || !(a <= 4.6e-38)) {
		tmp = x + y;
	} else {
		tmp = x + ((y / t) * (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -33500000000000.0) or not (a <= 4.6e-38):
		tmp = x + y
	else:
		tmp = x + ((y / t) * (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -33500000000000.0) || !(a <= 4.6e-38))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y / t) * Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -33500000000000.0) || ~((a <= 4.6e-38)))
		tmp = x + y;
	else
		tmp = x + ((y / t) * (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -33500000000000.0], N[Not[LessEqual[a, 4.6e-38]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.35e13 or 4.60000000000000003e-38 < a

   1. Initial program 81.9%

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

   3. Taylor expanded in a around inf 74.7%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 74.7%

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

   5. Simplified 74.7%

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

   if -3.35e13 < a < 4.60000000000000003e-38

   1. Initial program 74.5%

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

   3. Taylor expanded in t around inf 87.0%

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

      1. associate--l+ 87.0%

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

      2. distribute-lft-out-- 87.0%

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

      3. div-sub 87.0%

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

      4. mul-1-neg 87.0%

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

      5. unsub-neg 87.0%

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

      6. *-commutative 87.0%

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

      7. distribute-lft-out-- 87.0%

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

   5. Simplified 87.0%

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

   6. Taylor expanded in a around 0 87.0%

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

      1. mul-1-neg 87.0%

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

      2. sub-neg 87.0%

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

      3. associate--l- 87.0%

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

      4. +-commutative 87.0%

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

      5. associate--l- 87.0%

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

      6. cancel-sign-sub-inv 87.0%

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

      7. metadata-eval 87.0%

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

      8. associate-*r/ 86.3%

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

      9. *-lft-identity 86.3%

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

      10. associate-+r- 86.3%

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

      11. associate-*r/ 87.0%

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

      12. *-commutative 87.0%

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

      13. associate-*r/ 87.7%

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

      14. associate-/l* 84.8%

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

      15. distribute-rgt-out-- 87.7%

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

   8. Simplified 87.7%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -33500000000000 \lor \neg \left(a \leq 4.6 \cdot 10^{-38}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-17} \lor \neg \left(t \leq 1700000\right):\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.75e-17) (not (<= t 1700000.0)))
   (+ x (* (/ y t) (- z a)))
   (- (+ x y) (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.75e-17) || !(t <= 1700000.0)) {
		tmp = x + ((y / t) * (z - a));
	} else {
		tmp = (x + y) - (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.75d-17)) .or. (.not. (t <= 1700000.0d0))) then
        tmp = x + ((y / t) * (z - a))
    else
        tmp = (x + y) - (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.75e-17) || !(t <= 1700000.0)) {
		tmp = x + ((y / t) * (z - a));
	} else {
		tmp = (x + y) - (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.75e-17) or not (t <= 1700000.0):
		tmp = x + ((y / t) * (z - a))
	else:
		tmp = (x + y) - (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.75e-17) || !(t <= 1700000.0))
		tmp = Float64(x + Float64(Float64(y / t) * Float64(z - a)));
	else
		tmp = Float64(Float64(x + y) - Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.75e-17) || ~((t <= 1700000.0)))
		tmp = x + ((y / t) * (z - a));
	else
		tmp = (x + y) - (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.75e-17], N[Not[LessEqual[t, 1700000.0]], $MachinePrecision]], N[(x + N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.7500000000000001e-17 or 1.7e6 < t

   1. Initial program 61.2%

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

   3. Taylor expanded in t around inf 86.0%

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

      1. associate--l+ 86.0%

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

      2. distribute-lft-out-- 86.0%

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

      3. div-sub 86.0%

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

      4. mul-1-neg 86.0%

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

      5. unsub-neg 86.0%

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

      6. *-commutative 86.0%

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

      7. distribute-lft-out-- 86.1%

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

   5. Simplified 86.1%

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

   6. Taylor expanded in a around 0 86.0%

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

      1. mul-1-neg 86.0%

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

      2. sub-neg 86.0%

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

      3. associate--l- 86.0%

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

      4. +-commutative 86.0%

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

      5. associate--l- 86.0%

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

      6. cancel-sign-sub-inv 86.0%

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

      7. metadata-eval 86.0%

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

      8. associate-*r/ 89.0%

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

      9. *-lft-identity 89.0%

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

      10. associate-+r- 89.0%

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

      11. associate-*r/ 86.0%

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

      12. *-commutative 86.0%

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

      13. associate-*r/ 89.1%

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

      14. associate-/l* 91.5%

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

      15. distribute-rgt-out-- 91.5%

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

   8. Simplified 91.5%

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

   if -1.7500000000000001e-17 < t < 1.7e6

   1. Initial program 93.3%

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

   3. Taylor expanded in t around 0 82.8%

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

      1. *-commutative 82.8%

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

      2. associate-/l* 87.7%

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

   5. Applied egg-rr 87.7%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-17} \lor \neg \left(t \leq 1700000\right):\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+14} \lor \neg \left(a \leq 4.3 \cdot 10^{-5}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.4e+14) (not (<= a 4.3e-5))) (+ x y) (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.4e+14) || !(a <= 4.3e-5)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.4d+14)) .or. (.not. (a <= 4.3d-5))) then
        tmp = x + y
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.4e+14) || !(a <= 4.3e-5)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.4e+14) or not (a <= 4.3e-5):
		tmp = x + y
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.4e+14) || !(a <= 4.3e-5))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.4e+14) || ~((a <= 4.3e-5)))
		tmp = x + y;
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.4e+14], N[Not[LessEqual[a, 4.3e-5]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.4e14 or 4.3000000000000002e-5 < a

   1. Initial program 81.3%

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

   3. Taylor expanded in a around inf 75.4%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 75.4%

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

   5. Simplified 75.4%

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

   if -3.4e14 < a < 4.3000000000000002e-5

   1. Initial program 75.2%

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

   3. Taylor expanded in t around inf 86.0%

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

      1. associate--l+ 86.0%

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

      2. distribute-lft-out-- 86.0%

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

      3. div-sub 86.0%

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

      4. mul-1-neg 86.0%

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

      5. unsub-neg 86.0%

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

      6. *-commutative 86.0%

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

      7. distribute-lft-out-- 86.0%

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

   5. Simplified 86.0%

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

   6. Taylor expanded in a around 0 84.7%

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

      1. cancel-sign-sub-inv 84.7%

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

      2. metadata-eval 84.7%

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

      3. associate-*r/ 84.0%

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

      4. *-lft-identity 84.0%

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

   8. Simplified 84.0%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+14} \lor \neg \left(a \leq 4.3 \cdot 10^{-5}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -950000000000 \lor \neg \left(a \leq 4.8 \cdot 10^{-65}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -950000000000.0) (not (<= a 4.8e-65))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -950000000000.0) || !(a <= 4.8e-65)) {
		tmp = x + y;
	} 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 <= (-950000000000.0d0)) .or. (.not. (a <= 4.8d-65))) then
        tmp = x + y
    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 <= -950000000000.0) || !(a <= 4.8e-65)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -950000000000.0) or not (a <= 4.8e-65):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -950000000000.0) || !(a <= 4.8e-65))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -950000000000.0) || ~((a <= 4.8e-65)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -950000000000.0], N[Not[LessEqual[a, 4.8e-65]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -9.5e11 or 4.8000000000000003e-65 < a

   1. Initial program 82.7%

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

   3. Taylor expanded in a around inf 73.7%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 73.7%

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

   5. Simplified 73.7%

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

   if -9.5e11 < a < 4.8000000000000003e-65

   1. Initial program 73.5%

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

   3. Taylor expanded in x around inf 59.2%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -950000000000 \lor \neg \left(a \leq 4.8 \cdot 10^{-65}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.1% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.8%

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

3. Taylor expanded in x around inf 56.9%

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

4. Final simplification 56.9%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 88.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (< t_2 -1.3664970889390727e-7)
     t_1
     (if (< t_2 1.4754293444577233e-239)
       (/ (- (* y (- a z)) (* x t)) (- a t))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - 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) :: t_2
    real(8) :: tmp
    t_1 = (y + x) - (((z - t) * (1.0d0 / (a - t))) * y)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 < (-1.3664970889390727d-7)) then
        tmp = t_1
    else if (t_2 < 1.4754293444577233d-239) then
        tmp = ((y * (a - z)) - (x * t)) / (a - 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 + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 < -1.3664970889390727e-7:
		tmp = t_1
	elif t_2 < 1.4754293444577233e-239:
		tmp = ((y * (a - z)) - (x * t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) - Float64(Float64(Float64(z - t) * Float64(1.0 / Float64(a - t))) * y))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = Float64(Float64(Float64(y * Float64(a - z)) - Float64(x * t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.3664970889390727e-7], t$95$1, If[Less[t$95$2, 1.4754293444577233e-239], N[(N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024112 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-7) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y))))

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