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

Percentage Accurate: 76.7% → 87.5%

Time: 6.9s

Alternatives: 9

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: 76.7% 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: 87.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z\right) \cdot \frac{y}{a - t}\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-256}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+300}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z) (/ y (- a t))))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-256)
       t_2
       (if (<= t_2 0.0)
         (- x (/ (* y (- a z)) t))
         (if (<= t_2 5e+300) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -z * (y / (a - t));
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-256) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = x - ((y * (a - z)) / t);
	} else if (t_2 <= 5e+300) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -z * (y / (a - t));
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-256) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = x - ((y * (a - z)) / t);
	} else if (t_2 <= 5e+300) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -z * (y / (a - t))
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-256:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = x - ((y * (a - z)) / t)
	elif t_2 <= 5e+300:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-z) * Float64(y / 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 = t_1;
	elseif (t_2 <= -2e-256)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	elseif (t_2 <= 5e+300)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -z * (y / (a - t));
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-256)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = x - ((y * (a - z)) / t);
	elseif (t_2 <= 5e+300)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-z) * N[(y / 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)], t$95$1, If[LessEqual[t$95$2, -2e-256], t$95$2, If[LessEqual[t$95$2, 0.0], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+300], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -inf.0 or 5.00000000000000026e300 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 36.9%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. associate-*r* N/A

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

      3. associate-*l/ N/A

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

      6. mul-1-neg N/A

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

      7. distribute-rgt-neg-out N/A

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

      8. distribute-lft-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 70.5

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

   5. Applied rewrites 70.5%

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

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -1.99999999999999995e-256 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 5.00000000000000026e300

   1. Initial program 98.3%

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

   if -1.99999999999999995e-256 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 4.3%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. +-commutative N/A

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

      11. *-lft-identity N/A

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

      12. metadata-eval N/A

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

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

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

      14. distribute-lft-out-- N/A

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

      15. mul-1-neg N/A

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

      16. distribute-neg-frac N/A

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

   5. Applied rewrites 99.9%

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

Alternative 2: 64.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+300}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+300)))
     (* y (/ z 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)) || !(t_1 <= 5e+300)) {
		tmp = y * (z / 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) || !(t_1 <= 5e+300)) {
		tmp = y * (z / 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) or not (t_1 <= 5e+300):
		tmp = y * (z / 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)) || !(t_1 <= 5e+300))
		tmp = Float64(y * Float64(z / 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) || ~((t_1 <= 5e+300)))
		tmp = y * (z / 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[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+300]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -inf.0 or 5.00000000000000026e300 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 36.9%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. +-commutative N/A

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

      11. *-lft-identity N/A

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

      12. metadata-eval N/A

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

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

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

      14. distribute-lft-out-- N/A

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

      15. mul-1-neg N/A

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

      16. distribute-neg-frac N/A

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

   5. Applied rewrites 40.5%

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

   6. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 45.0

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

   8. Applied rewrites 45.0%

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

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 5.00000000000000026e300

   1. Initial program 91.2%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 73.9

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

   5. Applied rewrites 73.9%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \leq -\infty \lor \neg \left(\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \leq 5 \cdot 10^{+300}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+236}:\\ \;\;\;\;x - \mathsf{fma}\left(\frac{-y}{a}, \frac{z}{t}, \frac{y}{t}\right) \cdot a\\ \mathbf{elif}\;t \leq 10^{+166}:\\ \;\;\;\;\left(x + y\right) - \frac{a + t}{a - t} \cdot \left(\left(z - t\right) \cdot \frac{y}{a + t}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{z}{x \cdot t} - -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.4e+236)
   (- x (* (fma (/ (- y) a) (/ z t) (/ y t)) a))
   (if (<= t 1e+166)
     (- (+ x y) (* (/ (+ a t) (- a t)) (* (- z t) (/ y (+ a t)))))
     (* x (- (* y (/ z (* x t))) -1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.4e+236) {
		tmp = x - (fma((-y / a), (z / t), (y / t)) * a);
	} else if (t <= 1e+166) {
		tmp = (x + y) - (((a + t) / (a - t)) * ((z - t) * (y / (a + t))));
	} else {
		tmp = x * ((y * (z / (x * t))) - -1.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.4e+236)
		tmp = Float64(x - Float64(fma(Float64(Float64(-y) / a), Float64(z / t), Float64(y / t)) * a));
	elseif (t <= 1e+166)
		tmp = Float64(Float64(x + y) - Float64(Float64(Float64(a + t) / Float64(a - t)) * Float64(Float64(z - t) * Float64(y / Float64(a + t)))));
	else
		tmp = Float64(x * Float64(Float64(y * Float64(z / Float64(x * t))) - -1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.4e+236], N[(x - N[(N[(N[((-y) / a), $MachinePrecision] * N[(z / t), $MachinePrecision] + N[(y / t), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+166], N[(N[(x + y), $MachinePrecision] - N[(N[(N[(a + t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] * N[(y / N[(a + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * N[(z / N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.40000000000000028e236

   1. Initial program 24.7%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. +-commutative N/A

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

      11. *-lft-identity N/A

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

      12. metadata-eval N/A

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

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

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

      14. distribute-lft-out-- N/A

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

      15. mul-1-neg N/A

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

      16. distribute-neg-frac N/A

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

   5. Applied rewrites 55.4%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r* N/A

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

      5. times-frac N/A

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

      6. associate-*r/ N/A

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

      7. lower-fma.f64 N/A

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

      8. associate-*r/ N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-/.f64 92.3

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

   8. Applied rewrites 92.3%

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

   if -7.40000000000000028e236 < t < 9.9999999999999994e165

   1. Initial program 85.8%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. flip-- N/A

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

      4. associate-/r/ N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. difference-of-squares N/A

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

      8. lift--.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-+.f64 76.3

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

   4. Applied rewrites 76.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. times-frac N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 91.0

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

   6. Applied rewrites 91.0%

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

   if 9.9999999999999994e165 < t

   1. Initial program 43.9%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. +-commutative N/A

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

      11. *-lft-identity N/A

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

      12. metadata-eval N/A

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

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

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

      14. distribute-lft-out-- N/A

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

      15. mul-1-neg N/A

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

      16. distribute-neg-frac N/A

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

   5. Applied rewrites 80.0%

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

   6. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. distribute-lft-neg-in N/A

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

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

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

      5. associate-/l* N/A

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

      6. +-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 80.0

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

   8. Applied rewrites 80.0%

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

   9. Taylor expanded in x around -inf

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

       1. mul-1-neg N/A

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

       2. distribute-lft-neg-in N/A

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

       3. lower-*.f64 N/A

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

       4. lower-neg.f64 N/A

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

       5. lower--.f64 N/A

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

       6. mul-1-neg N/A

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

       7. associate-/l* N/A

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

       8. distribute-lft-neg-in N/A

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

       9. mul-1-neg N/A

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

       10. lower-*.f64 N/A

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

       11. mul-1-neg N/A

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

       12. lower-neg.f64 N/A

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

       13. lower-/.f64 N/A

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

       14. *-commutative N/A

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

       15. lower-*.f64 89.5

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

   11. Applied rewrites 89.5%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+236}:\\ \;\;\;\;x - \mathsf{fma}\left(\frac{-y}{a}, \frac{z}{t}, \frac{y}{t}\right) \cdot a\\ \mathbf{elif}\;t \leq 10^{+166}:\\ \;\;\;\;\left(x + y\right) - \frac{a + t}{a - t} \cdot \left(\left(z - t\right) \cdot \frac{y}{a + t}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{z}{x \cdot t} - -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-58} \lor \neg \left(a \leq 2.4 \cdot 10^{-75}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, -y, y + x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.7e-58) (not (<= a 2.4e-75)))
   (fma (/ z a) (- y) (+ y x))
   (- x (/ (* y (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.7e-58) || !(a <= 2.4e-75)) {
		tmp = fma((z / a), -y, (y + x));
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.7e-58) || !(a <= 2.4e-75))
		tmp = fma(Float64(z / a), Float64(-y), Float64(y + x));
	else
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.7e-58], N[Not[LessEqual[a, 2.4e-75]], $MachinePrecision]], N[(N[(z / a), $MachinePrecision] * (-y) + N[(y + x), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.69999999999999987e-58 or 2.40000000000000019e-75 < a

   1. Initial program 83.4%

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

   3. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

      4. associate-*r/ N/A

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

      5. mul-1-neg N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. distribute-rgt-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. mul-1-neg N/A

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

      14. lower-neg.f64 N/A

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

      15. +-commutative N/A

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

      16. lower-+.f64 79.8

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

   5. Applied rewrites 79.8%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\frac{z}{a}, -y, y + x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 85.0%

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

   if -1.69999999999999987e-58 < a < 2.40000000000000019e-75

   1. Initial program 73.0%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. +-commutative N/A

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

      11. *-lft-identity N/A

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

      12. metadata-eval N/A

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

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

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

      14. distribute-lft-out-- N/A

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

      15. mul-1-neg N/A

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

      16. distribute-neg-frac N/A

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

   5. Applied rewrites 79.6%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-58} \lor \neg \left(a \leq 2.4 \cdot 10^{-75}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, -y, y + x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -90000000 \lor \neg \left(a \leq 7.5 \cdot 10^{-64}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -90000000.0) (not (<= a 7.5e-64)))
   (+ y x)
   (- x (/ (* y (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -90000000.0) || !(a <= 7.5e-64)) {
		tmp = y + x;
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	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 <= (-90000000.0d0)) .or. (.not. (a <= 7.5d-64))) then
        tmp = y + x
    else
        tmp = x - ((y * (a - 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 <= -90000000.0) || !(a <= 7.5e-64)) {
		tmp = y + x;
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -90000000.0) or not (a <= 7.5e-64):
		tmp = y + x
	else:
		tmp = x - ((y * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -90000000.0) || !(a <= 7.5e-64))
		tmp = Float64(y + x);
	else
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -90000000.0) || ~((a <= 7.5e-64)))
		tmp = y + x;
	else
		tmp = x - ((y * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -90000000.0], N[Not[LessEqual[a, 7.5e-64]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -9e7 or 7.49999999999999949e-64 < a

   1. Initial program 83.9%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 77.0

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

   5. Applied rewrites 77.0%

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

   if -9e7 < a < 7.49999999999999949e-64

   1. Initial program 74.2%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. +-commutative N/A

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

      11. *-lft-identity N/A

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

      12. metadata-eval N/A

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

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

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

      14. distribute-lft-out-- N/A

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

      15. mul-1-neg N/A

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

      16. distribute-neg-frac N/A

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

   5. Applied rewrites 75.3%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -90000000 \lor \neg \left(a \leq 7.5 \cdot 10^{-64}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+42} \lor \neg \left(a \leq 5.4 \cdot 10^{-30}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2e+42) (not (<= a 5.4e-30))) (+ y x) (fma y (/ z t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2e+42) || !(a <= 5.4e-30)) {
		tmp = y + x;
	} else {
		tmp = fma(y, (z / t), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2e+42) || !(a <= 5.4e-30))
		tmp = Float64(y + x);
	else
		tmp = fma(y, Float64(z / t), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2e+42], N[Not[LessEqual[a, 5.4e-30]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.00000000000000009e42 or 5.39999999999999975e-30 < a

   1. Initial program 84.5%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 77.6

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

   5. Applied rewrites 77.6%

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

   if -2.00000000000000009e42 < a < 5.39999999999999975e-30

   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

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. +-commutative N/A

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

      11. *-lft-identity N/A

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

      12. metadata-eval N/A

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

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

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

      14. distribute-lft-out-- N/A

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

      15. mul-1-neg N/A

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

      16. distribute-neg-frac N/A

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

   5. Applied rewrites 74.0%

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

   6. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. distribute-lft-neg-in N/A

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

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

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

      5. associate-/l* N/A

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

      6. +-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 73.1

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

   8. Applied rewrites 73.1%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+42} \lor \neg \left(a \leq 5.4 \cdot 10^{-30}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.6% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+177}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= t -1.5e+177) x (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.5e+177) {
		tmp = 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 (t <= (-1.5d+177)) then
        tmp = 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 (t <= -1.5e+177) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.5e+177:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.5e+177)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.5e+177)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.5e+177], x, N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.5e177

   1. Initial program 46.8%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 59.9%

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

   if -1.5e177 < t

   1. Initial program 83.0%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 63.4

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

   5. Applied rewrites 63.4%

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

Alternative 8: 52.3% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.4 \cdot 10^{+147}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= y 5.4e+147) x y))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 5.4e+147) {
		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 <= 5.4d+147) 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 <= 5.4e+147) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 5.4e+147:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 5.4e+147)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 5.4e+147)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 5.4e+147], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 5.39999999999999995e147

   1. Initial program 81.8%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 54.9%

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

   if 5.39999999999999995e147 < y

   1. Initial program 62.8%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 56.0

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

   5. Applied rewrites 56.0%

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

   6. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 47.8

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

   8. Applied rewrites 47.8%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 49.0%

       \[\leadsto y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 51.2% 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 79.6%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 50.6%

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

Developer Target 1: 87.7% 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

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 + 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 2025026 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -13664970889390727/100000000000000000000000) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 14754293444577233/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)))))

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