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

Percentage Accurate: 76.9% → 91.0%

Time: 3.9s

Alternatives: 12

Speedup: 0.8×

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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: 76.9% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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: 91.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ t_2 := \frac{z}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(\left(\left(\frac{t}{a - t} + 1\right) + \frac{x}{y}\right) - t\_2\right) \cdot y\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-198}:\\ \;\;\;\;\frac{y \cdot z - a \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* (- z t) y) (- a t)))) (t_2 (/ z (- a t))))
   (if (<= t_1 (- INFINITY))
     (* (- (+ (+ (/ t (- a t)) 1.0) (/ x y)) t_2) y)
     (if (<= t_1 -5e-181)
       t_1
       (if (<= t_1 2e-198)
         (+ (/ (- (* y z) (* a y)) t) x)
         (- (+ x y) (* y t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (((z - t) * y) / (a - t));
	double t_2 = z / (a - t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = ((((t / (a - t)) + 1.0) + (x / y)) - t_2) * y;
	} else if (t_1 <= -5e-181) {
		tmp = t_1;
	} else if (t_1 <= 2e-198) {
		tmp = (((y * z) - (a * y)) / t) + x;
	} else {
		tmp = (x + y) - (y * t_2);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (((z - t) * y) / (a - t));
	double t_2 = z / (a - t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = ((((t / (a - t)) + 1.0) + (x / y)) - t_2) * y;
	} else if (t_1 <= -5e-181) {
		tmp = t_1;
	} else if (t_1 <= 2e-198) {
		tmp = (((y * z) - (a * y)) / t) + x;
	} else {
		tmp = (x + y) - (y * t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (((z - t) * y) / (a - t))
	t_2 = z / (a - t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = ((((t / (a - t)) + 1.0) + (x / y)) - t_2) * y
	elif t_1 <= -5e-181:
		tmp = t_1
	elif t_1 <= 2e-198:
		tmp = (((y * z) - (a * y)) / t) + x
	else:
		tmp = (x + y) - (y * t_2)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	t_2 = Float64(z / Float64(a - t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(Float64(t / Float64(a - t)) + 1.0) + Float64(x / y)) - t_2) * y);
	elseif (t_1 <= -5e-181)
		tmp = t_1;
	elseif (t_1 <= 2e-198)
		tmp = Float64(Float64(Float64(Float64(y * z) - Float64(a * y)) / t) + x);
	else
		tmp = Float64(Float64(x + y) - Float64(y * t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - (((z - t) * y) / (a - t));
	t_2 = z / (a - t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = ((((t / (a - t)) + 1.0) + (x / y)) - t_2) * y;
	elseif (t_1 <= -5e-181)
		tmp = t_1;
	elseif (t_1 <= 2e-198)
		tmp = (((y * z) - (a * y)) / t) + x;
	else
		tmp = (x + y) - (y * t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(N[(N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, -5e-181], t$95$1, If[LessEqual[t$95$1, 2e-198], N[(N[(N[(N[(y * z), $MachinePrecision] - N[(a * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 35.0%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-+r+ N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 87.0

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

   4. Applied rewrites 87.0%

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

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -5.0000000000000001e-181

   1. Initial program 98.1%

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

   if -5.0000000000000001e-181 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 1.9999999999999998e-198

   1. Initial program 24.9%

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

   2. Taylor expanded in t around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. fp-cancel-sub-sign-inv N/A

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

      7. mul-1-neg N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. associate-*r* N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. lower-neg.f64 86.6

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

   4. Applied rewrites 86.6%

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

   5. Taylor expanded in z around 0

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

      1. sub-div N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 86.6

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

   7. Applied rewrites 86.6%

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

   if 1.9999999999999998e-198 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 82.6%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 87.7

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

   4. Applied rewrites 87.7%

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

Alternative 2: 89.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a - t}\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;x - t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-181}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-198}:\\ \;\;\;\;\frac{y \cdot z - a \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- a t)))) (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_2 (- INFINITY))
     (- x t_1)
     (if (<= t_2 -5e-181)
       t_2
       (if (<= t_2 2e-198) (+ (/ (- (* y z) (* a y)) t) x) (- (+ x y) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = x - t_1;
	} else if (t_2 <= -5e-181) {
		tmp = t_2;
	} else if (t_2 <= 2e-198) {
		tmp = (((y * z) - (a * y)) / t) + x;
	} else {
		tmp = (x + y) - t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = x - t_1;
	} else if (t_2 <= -5e-181) {
		tmp = t_2;
	} else if (t_2 <= 2e-198) {
		tmp = (((y * z) - (a * y)) / t) + x;
	} else {
		tmp = (x + y) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (a - t))
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = x - t_1
	elif t_2 <= -5e-181:
		tmp = t_2
	elif t_2 <= 2e-198:
		tmp = (((y * z) - (a * y)) / t) + x
	else:
		tmp = (x + y) - t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(a - t)))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(x - t_1);
	elseif (t_2 <= -5e-181)
		tmp = t_2;
	elseif (t_2 <= 2e-198)
		tmp = Float64(Float64(Float64(Float64(y * z) - Float64(a * y)) / t) + x);
	else
		tmp = Float64(Float64(x + y) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (a - t));
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = x - t_1;
	elseif (t_2 <= -5e-181)
		tmp = t_2;
	elseif (t_2 <= 2e-198)
		tmp = (((y * z) - (a * y)) / t) + x;
	else
		tmp = (x + y) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $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[LessEqual[t$95$2, (-Infinity)], N[(x - t$95$1), $MachinePrecision], If[LessEqual[t$95$2, -5e-181], t$95$2, If[LessEqual[t$95$2, 2e-198], N[(N[(N[(N[(y * z), $MachinePrecision] - N[(a * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 35.0%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 66.0

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

   4. Applied rewrites 66.0%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 74.4%

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

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -5.0000000000000001e-181

   1. Initial program 98.1%

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

   if -5.0000000000000001e-181 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 1.9999999999999998e-198

   1. Initial program 24.9%

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

   2. Taylor expanded in t around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. fp-cancel-sub-sign-inv N/A

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

      7. mul-1-neg N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. associate-*r* N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. lower-neg.f64 86.6

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

   4. Applied rewrites 86.6%

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

   5. Taylor expanded in z around 0

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

      1. sub-div N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 86.6

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

   7. Applied rewrites 86.6%

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

   if 1.9999999999999998e-198 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 82.6%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 87.7

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

   4. Applied rewrites 87.7%

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

Alternative 3: 88.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - y \cdot \frac{z}{a - t}\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-198}:\\ \;\;\;\;\frac{y \cdot z - a \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (* y (/ z (- a t)))))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_2 -5e-181)
     t_1
     (if (<= t_2 2e-198) (+ (/ (- (* y z) (* a y)) t) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (y * (z / (a - t)));
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -5e-181) {
		tmp = t_1;
	} else if (t_2 <= 2e-198) {
		tmp = (((y * z) - (a * y)) / t) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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) - (y * (z / (a - t)))
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 <= (-5d-181)) then
        tmp = t_1
    else if (t_2 <= 2d-198) then
        tmp = (((y * z) - (a * y)) / t) + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (y * (z / (a - t)));
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -5e-181) {
		tmp = t_1;
	} else if (t_2 <= 2e-198) {
		tmp = (((y * z) - (a * y)) / t) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (y * (z / (a - t)))
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 <= -5e-181:
		tmp = t_1
	elif t_2 <= 2e-198:
		tmp = (((y * z) - (a * y)) / t) + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(y * Float64(z / Float64(a - t))))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -5e-181)
		tmp = t_1;
	elseif (t_2 <= 2e-198)
		tmp = Float64(Float64(Float64(Float64(y * z) - Float64(a * y)) / t) + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - (y * (z / (a - t)));
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 <= -5e-181)
		tmp = t_1;
	elseif (t_2 <= 2e-198)
		tmp = (((y * z) - (a * y)) / t) + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $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[LessEqual[t$95$2, -5e-181], t$95$1, If[LessEqual[t$95$2, 2e-198], N[(N[(N[(N[(y * z), $MachinePrecision] - N[(a * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -5.0000000000000001e-181 or 1.9999999999999998e-198 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 82.2%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 87.4

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

   4. Applied rewrites 87.4%

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

   if -5.0000000000000001e-181 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 1.9999999999999998e-198

   1. Initial program 24.9%

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

   2. Taylor expanded in t around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. fp-cancel-sub-sign-inv N/A

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

      7. mul-1-neg N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. associate-*r* N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. lower-neg.f64 86.6

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

   4. Applied rewrites 86.6%

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

   5. Taylor expanded in z around 0

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

      1. sub-div N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 86.6

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

   7. Applied rewrites 86.6%

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

Alternative 4: 87.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a - t}\\ t_2 := \left(x + y\right) - t\_1\\ \mathbf{if}\;a \leq -2700000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 84000000:\\ \;\;\;\;x - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- a t)))) (t_2 (- (+ x y) t_1)))
   (if (<= a -2700000000.0) t_2 (if (<= a 84000000.0) (- x t_1) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double t_2 = (x + y) - t_1;
	double tmp;
	if (a <= -2700000000.0) {
		tmp = t_2;
	} else if (a <= 84000000.0) {
		tmp = x - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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 * (z / (a - t))
    t_2 = (x + y) - t_1
    if (a <= (-2700000000.0d0)) then
        tmp = t_2
    else if (a <= 84000000.0d0) then
        tmp = x - 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 = y * (z / (a - t));
	double t_2 = (x + y) - t_1;
	double tmp;
	if (a <= -2700000000.0) {
		tmp = t_2;
	} else if (a <= 84000000.0) {
		tmp = x - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (a - t))
	t_2 = (x + y) - t_1
	tmp = 0
	if a <= -2700000000.0:
		tmp = t_2
	elif a <= 84000000.0:
		tmp = x - t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(a - t)))
	t_2 = Float64(Float64(x + y) - t_1)
	tmp = 0.0
	if (a <= -2700000000.0)
		tmp = t_2;
	elseif (a <= 84000000.0)
		tmp = Float64(x - t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (a - t));
	t_2 = (x + y) - t_1;
	tmp = 0.0;
	if (a <= -2700000000.0)
		tmp = t_2;
	elseif (a <= 84000000.0)
		tmp = x - t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[a, -2700000000.0], t$95$2, If[LessEqual[a, 84000000.0], N[(x - t$95$1), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.7e9 or 8.4e7 < a

   1. Initial program 79.0%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 89.5

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

   4. Applied rewrites 89.5%

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

   if -2.7e9 < a < 8.4e7

   1. Initial program 74.8%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 73.7

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

   4. Applied rewrites 73.7%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 87.7%

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

Alternative 5: 83.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -15500000000000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+91}:\\ \;\;\;\;x - y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -15500000000000.0)
   (+ y x)
   (if (<= a 4e+91) (- x (* y (/ z (- a t)))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -15500000000000.0) {
		tmp = y + x;
	} else if (a <= 4e+91) {
		tmp = x - (y * (z / (a - t)));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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 <= (-15500000000000.0d0)) then
        tmp = y + x
    else if (a <= 4d+91) then
        tmp = x - (y * (z / (a - t)))
    else
        tmp = y + 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 <= -15500000000000.0) {
		tmp = y + x;
	} else if (a <= 4e+91) {
		tmp = x - (y * (z / (a - t)));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -15500000000000.0:
		tmp = y + x
	elif a <= 4e+91:
		tmp = x - (y * (z / (a - t)))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -15500000000000.0)
		tmp = Float64(y + x);
	elseif (a <= 4e+91)
		tmp = Float64(x - Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -15500000000000.0)
		tmp = y + x;
	elseif (a <= 4e+91)
		tmp = x - (y * (z / (a - t)));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -15500000000000.0], N[(y + x), $MachinePrecision], If[LessEqual[a, 4e+91], N[(x - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.55e13 or 4.00000000000000032e91 < a

   1. Initial program 79.3%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 79.3

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

   4. Applied rewrites 79.3%

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

   if -1.55e13 < a < 4.00000000000000032e91

   1. Initial program 75.1%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 74.8

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

   4. Applied rewrites 74.8%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 86.3%

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

Alternative 6: 76.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -15500000000000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.685 \cdot 10^{-9}:\\ \;\;\;\;x - y \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -15500000000000.0)
   (+ y x)
   (if (<= a 1.685e-9) (- x (* y (/ z (- t)))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -15500000000000.0) {
		tmp = y + x;
	} else if (a <= 1.685e-9) {
		tmp = x - (y * (z / -t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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 <= (-15500000000000.0d0)) then
        tmp = y + x
    else if (a <= 1.685d-9) then
        tmp = x - (y * (z / -t))
    else
        tmp = y + 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 <= -15500000000000.0) {
		tmp = y + x;
	} else if (a <= 1.685e-9) {
		tmp = x - (y * (z / -t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -15500000000000.0:
		tmp = y + x
	elif a <= 1.685e-9:
		tmp = x - (y * (z / -t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -15500000000000.0)
		tmp = Float64(y + x);
	elseif (a <= 1.685e-9)
		tmp = Float64(x - Float64(y * Float64(z / Float64(-t))));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -15500000000000.0)
		tmp = y + x;
	elseif (a <= 1.685e-9)
		tmp = x - (y * (z / -t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -15500000000000.0], N[(y + x), $MachinePrecision], If[LessEqual[a, 1.685e-9], N[(x - N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.55e13 or 1.68500000000000007e-9 < a

   1. Initial program 79.0%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 76.4

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

   4. Applied rewrites 76.4%

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

   if -1.55e13 < a < 1.68500000000000007e-9

   1. Initial program 74.7%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 73.7

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

   4. Applied rewrites 73.7%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 87.7%

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

   8. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 76.8

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

   10. Applied rewrites 76.8%

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

Alternative 7: 75.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -15500000000000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.685 \cdot 10^{-9}:\\ \;\;\;\;\frac{y \cdot z}{t} + x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -15500000000000.0)
   (+ y x)
   (if (<= a 1.685e-9) (+ (/ (* y z) t) x) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -15500000000000.0) {
		tmp = y + x;
	} else if (a <= 1.685e-9) {
		tmp = ((y * z) / t) + x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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 <= (-15500000000000.0d0)) then
        tmp = y + x
    else if (a <= 1.685d-9) then
        tmp = ((y * z) / t) + x
    else
        tmp = y + 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 <= -15500000000000.0) {
		tmp = y + x;
	} else if (a <= 1.685e-9) {
		tmp = ((y * z) / t) + x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -15500000000000.0:
		tmp = y + x
	elif a <= 1.685e-9:
		tmp = ((y * z) / t) + x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -15500000000000.0)
		tmp = Float64(y + x);
	elseif (a <= 1.685e-9)
		tmp = Float64(Float64(Float64(y * z) / t) + x);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -15500000000000.0)
		tmp = y + x;
	elseif (a <= 1.685e-9)
		tmp = ((y * z) / t) + x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -15500000000000.0], N[(y + x), $MachinePrecision], If[LessEqual[a, 1.685e-9], N[(N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.55e13 or 1.68500000000000007e-9 < a

   1. Initial program 79.0%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 76.4

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

   4. Applied rewrites 76.4%

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

   if -1.55e13 < a < 1.68500000000000007e-9

   1. Initial program 74.7%

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

   2. Taylor expanded in t around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. fp-cancel-sub-sign-inv N/A

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

      7. mul-1-neg N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. associate-*r* N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. lower-neg.f64 78.4

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

   4. Applied rewrites 78.4%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 75.1

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

   7. Applied rewrites 75.1%

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

Alternative 8: 66.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-181}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-198}:\\ \;\;\;\;x - \frac{a \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (* y (/ z t))
     (if (<= t_1 -5e-181)
       (+ y x)
       (if (<= t_1 2e-198) (- x (/ (* a y) t)) (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * (z / t);
	} else if (t_1 <= -5e-181) {
		tmp = y + x;
	} else if (t_1 <= 2e-198) {
		tmp = x - ((a * y) / t);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (z / t);
	} else if (t_1 <= -5e-181) {
		tmp = y + x;
	} else if (t_1 <= 2e-198) {
		tmp = x - ((a * y) / t);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * (z / t)
	elif t_1 <= -5e-181:
		tmp = y + x
	elif t_1 <= 2e-198:
		tmp = x - ((a * y) / t)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(z / t));
	elseif (t_1 <= -5e-181)
		tmp = Float64(y + x);
	elseif (t_1 <= 2e-198)
		tmp = Float64(x - Float64(Float64(a * y) / t));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * (z / t);
	elseif (t_1 <= -5e-181)
		tmp = y + x;
	elseif (t_1 <= 2e-198)
		tmp = x - ((a * y) / t);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-181], N[(y + x), $MachinePrecision], If[LessEqual[t$95$1, 2e-198], N[(x - N[(N[(a * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 35.0%

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

   2. Taylor expanded in t around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. fp-cancel-sub-sign-inv N/A

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

      7. mul-1-neg N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. associate-*r* N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. lower-neg.f64 51.9

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

   4. Applied rewrites 51.9%

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

   5. Taylor expanded in y around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(-1, \frac{a}{t}, \frac{z}{t}\right) \]

      4. lower-/.f64 51.1

         \[\leadsto y \cdot \mathsf{fma}\left(-1, \frac{a}{t}, \frac{z}{t}\right) \]

   7. Applied rewrites 51.1%

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

   8. Taylor expanded in z around inf

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

      1. lift-/.f64 40.7

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

   10. Applied rewrites 40.7%

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

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -5.0000000000000001e-181 or 1.9999999999999998e-198 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 89.3%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 71.1

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

   4. Applied rewrites 71.1%

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

   if -5.0000000000000001e-181 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 1.9999999999999998e-198

   1. Initial program 24.9%

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

   2. Taylor expanded in t around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. fp-cancel-sub-sign-inv N/A

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

      7. mul-1-neg N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. associate-*r* N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. lower-neg.f64 86.6

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

   4. Applied rewrites 86.6%

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

   5. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 64.8

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

   7. Applied rewrites 64.8%

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

Alternative 9: 64.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-66}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-198}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (* y (/ z t))
     (if (<= t_1 -5e-66) (+ y x) (if (<= t_1 2e-198) x (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * (z / t);
	} else if (t_1 <= -5e-66) {
		tmp = y + x;
	} else if (t_1 <= 2e-198) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (z / t);
	} else if (t_1 <= -5e-66) {
		tmp = y + x;
	} else if (t_1 <= 2e-198) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * (z / t)
	elif t_1 <= -5e-66:
		tmp = y + x
	elif t_1 <= 2e-198:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(z / t));
	elseif (t_1 <= -5e-66)
		tmp = Float64(y + x);
	elseif (t_1 <= 2e-198)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * (z / t);
	elseif (t_1 <= -5e-66)
		tmp = y + x;
	elseif (t_1 <= 2e-198)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-66], N[(y + x), $MachinePrecision], If[LessEqual[t$95$1, 2e-198], x, N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 35.0%

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

   2. Taylor expanded in t around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. fp-cancel-sub-sign-inv N/A

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

      7. mul-1-neg N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. associate-*r* N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. lower-neg.f64 51.9

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

   4. Applied rewrites 51.9%

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

   5. Taylor expanded in y around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(-1, \frac{a}{t}, \frac{z}{t}\right) \]

      4. lower-/.f64 51.1

         \[\leadsto y \cdot \mathsf{fma}\left(-1, \frac{a}{t}, \frac{z}{t}\right) \]

   7. Applied rewrites 51.1%

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

   8. Taylor expanded in z around inf

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

      1. lift-/.f64 40.7

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

   10. Applied rewrites 40.7%

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

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -4.99999999999999962e-66 or 1.9999999999999998e-198 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 88.9%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 70.6

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

   4. Applied rewrites 70.6%

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

   if -4.99999999999999962e-66 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 1.9999999999999998e-198

   1. Initial program 47.6%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 51.2%

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

Alternative 10: 63.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+185}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+166}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.6e+185) x (if (<= t 5.6e+166) (+ y x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.6e+185) {
		tmp = x;
	} else if (t <= 5.6e+166) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.6d+185)) then
        tmp = x
    else if (t <= 5.6d+166) then
        tmp = y + x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.6e+185) {
		tmp = x;
	} else if (t <= 5.6e+166) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.6e+185:
		tmp = x
	elif t <= 5.6e+166:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.6e+185)
		tmp = x;
	elseif (t <= 5.6e+166)
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.6e+185)
		tmp = x;
	elseif (t <= 5.6e+166)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.6e+185], x, If[LessEqual[t, 5.6e+166], N[(y + x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -3.60000000000000029e185 or 5.59999999999999993e166 < t

   1. Initial program 49.4%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 67.4%

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

   if -3.60000000000000029e185 < t < 5.59999999999999993e166

   1. Initial program 84.7%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 62.5

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

   4. Applied rewrites 62.5%

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

Alternative 11: 53.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+184}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+134}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.4e+184) y (if (<= y 6.2e+134) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.4e+184) {
		tmp = y;
	} else if (y <= 6.2e+134) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-4.4d+184)) then
        tmp = y
    else if (y <= 6.2d+134) then
        tmp = x
    else
        tmp = 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 (y <= -4.4e+184) {
		tmp = y;
	} else if (y <= 6.2e+134) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.4e+184:
		tmp = y
	elif y <= 6.2e+134:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.4e+184)
		tmp = y;
	elseif (y <= 6.2e+134)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -4.4e+184)
		tmp = y;
	elseif (y <= 6.2e+134)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.4e+184], y, If[LessEqual[y, 6.2e+134], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4e184 or 6.19999999999999963e134 < y

   1. Initial program 52.7%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower--.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 60.9

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

   4. Applied rewrites 60.9%

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

   5. Taylor expanded in a around inf

      \[\leadsto y \]
   6. Step-by-step derivation

   7. Applied rewrites 32.1%

      \[\leadsto y \]

   if -4.4e184 < y < 6.19999999999999963e134

   1. Initial program 84.5%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 60.8%

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

Alternative 12: 50.3% accurate, 29.0× 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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 76.9%

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

2. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
3. Step-by-step derivation

4. Applied rewrites 50.3%

   \[\leadsto \color{blue}{x} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025101 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64
  (- (+ x y) (/ (* (- z t) y) (- a t))))