Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.8% → 93.4%

Time: 6.2s

Alternatives: 21

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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, b)
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), intent (in) :: b
    code = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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, b)
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), intent (in) :: b
    code = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \left(b - y\right) \cdot z + y\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_3 := \frac{x}{t\_1} \cdot y - \left(a - t\right) \cdot \frac{z}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-220}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+301}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (+ (* (- b y) z) y))
       (t_2 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))
       (t_3 (- (* (/ x t_1) y) (* (- a t) (/ z t_1)))))
  (if (<= t_2 (- INFINITY))
    t_3
    (if (<= t_2 -1e-220)
      t_2
      (if (<= t_2 0.0)
        (/ (- t a) (- b y))
        (if (<= t_2 2e+301)
          t_2
          (if (<= t_2 INFINITY)
            t_3
            (- (/ t (- b y)) (/ a (- b y))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((b - y) * z) + y;
	double t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_3 = ((x / t_1) * y) - ((a - t) * (z / t_1));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -1e-220) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (t - a) / (b - y);
	} else if (t_2 <= 2e+301) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = (t / (b - y)) - (a / (b - y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((b - y) * z) + y;
	double t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_3 = ((x / t_1) * y) - ((a - t) * (z / t_1));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_2 <= -1e-220) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (t - a) / (b - y);
	} else if (t_2 <= 2e+301) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = (t / (b - y)) - (a / (b - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((b - y) * z) + y
	t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	t_3 = ((x / t_1) * y) - ((a - t) * (z / t_1))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif t_2 <= -1e-220:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = (t - a) / (b - y)
	elif t_2 <= 2e+301:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = t_3
	else:
		tmp = (t / (b - y)) - (a / (b - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(b - y) * z) + y)
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	t_3 = Float64(Float64(Float64(x / t_1) * y) - Float64(Float64(a - t) * Float64(z / t_1)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -1e-220)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	elseif (t_2 <= 2e+301)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((b - y) * z) + y;
	t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	t_3 = ((x / t_1) * y) - ((a - t) * (z / t_1));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif (t_2 <= -1e-220)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = (t - a) / (b - y);
	elseif (t_2 <= 2e+301)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = (t / (b - y)) - (a / (b - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(b - y), $MachinePrecision] * z), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x / t$95$1), $MachinePrecision] * y), $MachinePrecision] - N[(N[(a - t), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -1e-220], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+301], t$95$2, If[LessEqual[t$95$2, Infinity], t$95$3, N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 2.0000000000000001e301 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 66.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. add-flip N/A

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

      4. div-sub N/A

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

      5. lower--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift-+.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-+.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

   3. Applied rewrites 72.1%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -9.9999999999999999e-221 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.0000000000000001e301

   1. Initial program 66.8%

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

   if -9.9999999999999999e-221 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 66.8%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 50.9%

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

   4. Applied rewrites 50.9%

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

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

   1. Initial program 66.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower--.f64 N/A

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

   3. Applied rewrites 79.4%

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

   4. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \frac{t}{b - y} - \frac{a}{b - y} \]

      4. lower-/.f64 N/A

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

      5. lower--.f64 50.5%

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

   6. Applied rewrites 50.5%

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

Alternative 2: 92.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{z}{\left(b - y\right) \cdot z + y} \cdot \left(t - a\right) - \frac{x}{z - 1}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;t\_1 \leq 10^{+300}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))
       (t_2
        (- (* (/ z (+ (* (- b y) z) y)) (- t a)) (/ x (- z 1.0)))))
  (if (<= t_1 (- INFINITY))
    t_2
    (if (<= t_1 -1e-220)
      t_1
      (if (<= t_1 0.0)
        (/ (- t a) (- b y))
        (if (<= t_1 1e+300)
          t_1
          (if (<= t_1 INFINITY)
            t_2
            (- (/ t (- b y)) (/ a (- b y))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = ((z / (((b - y) * z) + y)) * (t - a)) - (x / (z - 1.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -1e-220) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (t - a) / (b - y);
	} else if (t_1 <= 1e+300) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = (t / (b - y)) - (a / (b - y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = ((z / (((b - y) * z) + y)) * (t - a)) - (x / (z - 1.0));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= -1e-220) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (t - a) / (b - y);
	} else if (t_1 <= 1e+300) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = (t / (b - y)) - (a / (b - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	t_2 = ((z / (((b - y) * z) + y)) * (t - a)) - (x / (z - 1.0))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= -1e-220:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (t - a) / (b - y)
	elif t_1 <= 1e+300:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = t_2
	else:
		tmp = (t / (b - y)) - (a / (b - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = Float64(Float64(Float64(z / Float64(Float64(Float64(b - y) * z) + y)) * Float64(t - a)) - Float64(x / Float64(z - 1.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -1e-220)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	elseif (t_1 <= 1e+300)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	t_2 = ((z / (((b - y) * z) + y)) * (t - a)) - (x / (z - 1.0));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= -1e-220)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (t - a) / (b - y);
	elseif (t_1 <= 1e+300)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = (t / (b - y)) - (a / (b - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(z / N[(N[(N[(b - y), $MachinePrecision] * z), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] * N[(t - a), $MachinePrecision]), $MachinePrecision] - N[(x / N[(z - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -1e-220], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+300], t$95$1, If[LessEqual[t$95$1, Infinity], t$95$2, N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 1.0000000000000001e300 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 66.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower--.f64 N/A

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

   3. Applied rewrites 79.4%

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

   4. Taylor expanded in y around -inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 71.3%

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

   6. Applied rewrites 71.3%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -9.9999999999999999e-221 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.0000000000000001e300

   1. Initial program 66.8%

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

   if -9.9999999999999999e-221 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 66.8%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 50.9%

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

   4. Applied rewrites 50.9%

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

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

   1. Initial program 66.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower--.f64 N/A

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

   3. Applied rewrites 79.4%

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

   4. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \frac{t}{b - y} - \frac{a}{b - y} \]

      4. lower-/.f64 N/A

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

      5. lower--.f64 50.5%

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

   6. Applied rewrites 50.5%

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

Alternative 3: 92.8% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

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, b)
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), intent (in) :: b
    code = ((t - a) / (b - (y - (y / z)))) - (-x * (y / (((b - y) * z) + y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 66.8%

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

   1. lift-/.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. +-commutative N/A

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

   4. div-add N/A

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

   5. lift-*.f64 N/A

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

   6. associate-/l* N/A

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

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

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

   8. lower--.f64 N/A

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

3. Applied rewrites 79.4%

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

   1. lift-/.f64 N/A

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

   2. div-flip N/A

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

   3. lower-unsound-/.f64 N/A

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

   4. lower-unsound-/.f64 79.3%

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

5. Applied rewrites 79.3%

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

   1. lift--.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. lift-/.f64 N/A

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

   5. mult-flip-rev N/A

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

   6. lower-/.f64 N/A

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

   7. lift--.f64 79.4%

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

   8. lift-/.f64 N/A

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

   9. lift-+.f64 N/A

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

   10. lift-*.f64 N/A

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

   11. add-to-fraction-rev N/A

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

   12. lift--.f64 N/A

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

   13. associate-+l- N/A

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

   14. lower--.f64 N/A

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

   15. lower--.f64 N/A

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

   16. lower-/.f64 93.4%

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

7. Applied rewrites 93.4%

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

Alternative 4: 90.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - \left(y - \frac{y}{z}\right)} - \left(-x\right) \cdot 1\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;t\_1 \leq 10^{+258}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))
       (t_2 (- (/ (- t a) (- b (- y (/ y z)))) (* (- x) 1.0))))
  (if (<= t_1 (- INFINITY))
    t_2
    (if (<= t_1 -1e-220)
      t_1
      (if (<= t_1 0.0)
        (/ (- t a) (- b y))
        (if (<= t_1 1e+258)
          t_1
          (if (<= t_1 INFINITY)
            t_2
            (- (/ t (- b y)) (/ a (- b y))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = ((t - a) / (b - (y - (y / z)))) - (-x * 1.0);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -1e-220) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (t - a) / (b - y);
	} else if (t_1 <= 1e+258) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = (t / (b - y)) - (a / (b - y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = ((t - a) / (b - (y - (y / z)))) - (-x * 1.0);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= -1e-220) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (t - a) / (b - y);
	} else if (t_1 <= 1e+258) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = (t / (b - y)) - (a / (b - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	t_2 = ((t - a) / (b - (y - (y / z)))) - (-x * 1.0)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= -1e-220:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (t - a) / (b - y)
	elif t_1 <= 1e+258:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = t_2
	else:
		tmp = (t / (b - y)) - (a / (b - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = Float64(Float64(Float64(t - a) / Float64(b - Float64(y - Float64(y / z)))) - Float64(Float64(-x) * 1.0))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -1e-220)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	elseif (t_1 <= 1e+258)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	t_2 = ((t - a) / (b - (y - (y / z)))) - (-x * 1.0);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= -1e-220)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (t - a) / (b - y);
	elseif (t_1 <= 1e+258)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = (t / (b - y)) - (a / (b - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - N[(y - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[((-x) * 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -1e-220], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+258], t$95$1, If[LessEqual[t$95$1, Infinity], t$95$2, N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 1.0000000000000001e258 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 66.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower--.f64 N/A

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

   3. Applied rewrites 79.4%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 79.3%

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

   5. Applied rewrites 79.3%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. mult-flip-rev N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 79.4%

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

      8. lift-/.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. add-to-fraction-rev N/A

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

      12. lift--.f64 N/A

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

      13. associate-+l- N/A

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

      14. lower--.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lower-/.f64 93.4%

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

   7. Applied rewrites 93.4%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 66.3%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -9.9999999999999999e-221 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.0000000000000001e258

   1. Initial program 66.8%

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

   if -9.9999999999999999e-221 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 66.8%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 50.9%

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

   4. Applied rewrites 50.9%

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

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

   1. Initial program 66.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower--.f64 N/A

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

   3. Applied rewrites 79.4%

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

   4. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \frac{t}{b - y} - \frac{a}{b - y} \]

      4. lower-/.f64 N/A

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

      5. lower--.f64 50.5%

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

   6. Applied rewrites 50.5%

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

Alternative 5: 90.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{z}{\left(b - y\right) \cdot z + y} \cdot \left(t - a\right) - \left(-x\right) \cdot 1\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;t\_1 \leq 10^{+300}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))
       (t_2 (- (* (/ z (+ (* (- b y) z) y)) (- t a)) (* (- x) 1.0))))
  (if (<= t_1 (- INFINITY))
    t_2
    (if (<= t_1 -1e-220)
      t_1
      (if (<= t_1 0.0)
        (/ (- t a) (- b y))
        (if (<= t_1 1e+300)
          t_1
          (if (<= t_1 INFINITY)
            t_2
            (- (/ t (- b y)) (/ a (- b y))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = ((z / (((b - y) * z) + y)) * (t - a)) - (-x * 1.0);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -1e-220) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (t - a) / (b - y);
	} else if (t_1 <= 1e+300) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = (t / (b - y)) - (a / (b - y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = ((z / (((b - y) * z) + y)) * (t - a)) - (-x * 1.0);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= -1e-220) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (t - a) / (b - y);
	} else if (t_1 <= 1e+300) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = (t / (b - y)) - (a / (b - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	t_2 = ((z / (((b - y) * z) + y)) * (t - a)) - (-x * 1.0)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= -1e-220:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (t - a) / (b - y)
	elif t_1 <= 1e+300:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = t_2
	else:
		tmp = (t / (b - y)) - (a / (b - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = Float64(Float64(Float64(z / Float64(Float64(Float64(b - y) * z) + y)) * Float64(t - a)) - Float64(Float64(-x) * 1.0))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -1e-220)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	elseif (t_1 <= 1e+300)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	t_2 = ((z / (((b - y) * z) + y)) * (t - a)) - (-x * 1.0);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= -1e-220)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (t - a) / (b - y);
	elseif (t_1 <= 1e+300)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = (t / (b - y)) - (a / (b - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(z / N[(N[(N[(b - y), $MachinePrecision] * z), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] * N[(t - a), $MachinePrecision]), $MachinePrecision] - N[((-x) * 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -1e-220], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+300], t$95$1, If[LessEqual[t$95$1, Infinity], t$95$2, N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 1.0000000000000001e300 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 66.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower--.f64 N/A

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

   3. Applied rewrites 79.4%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 59.7%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -9.9999999999999999e-221 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.0000000000000001e300

   1. Initial program 66.8%

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

   if -9.9999999999999999e-221 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 66.8%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 50.9%

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

   4. Applied rewrites 50.9%

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

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

   1. Initial program 66.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower--.f64 N/A

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

   3. Applied rewrites 79.4%

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

   4. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \frac{t}{b - y} - \frac{a}{b - y} \]

      4. lower-/.f64 N/A

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

      5. lower--.f64 50.5%

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

   6. Applied rewrites 50.5%

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

Alternative 6: 90.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := \left(b - y\right) \cdot z + y\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+110}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+85}:\\ \;\;\;\;\frac{z}{t\_1} \cdot \left(t - a\right) - \left(-x\right) \cdot \frac{y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (+ (* (- b y) z) y)))
  (if (<= z -2.8e+110)
    (/ (- t a) (- b y))
    (if (<= z 4e+85)
      (- (* (/ z t_1) (- t a)) (* (- x) (/ y t_1)))
      (- (/ t (- b y)) (/ a (- b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((b - y) * z) + y;
	double tmp;
	if (z <= -2.8e+110) {
		tmp = (t - a) / (b - y);
	} else if (z <= 4e+85) {
		tmp = ((z / t_1) * (t - a)) - (-x * (y / t_1));
	} else {
		tmp = (t / (b - y)) - (a / (b - 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, b)
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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((b - y) * z) + y
    if (z <= (-2.8d+110)) then
        tmp = (t - a) / (b - y)
    else if (z <= 4d+85) then
        tmp = ((z / t_1) * (t - a)) - (-x * (y / t_1))
    else
        tmp = (t / (b - y)) - (a / (b - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((b - y) * z) + y;
	double tmp;
	if (z <= -2.8e+110) {
		tmp = (t - a) / (b - y);
	} else if (z <= 4e+85) {
		tmp = ((z / t_1) * (t - a)) - (-x * (y / t_1));
	} else {
		tmp = (t / (b - y)) - (a / (b - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((b - y) * z) + y
	tmp = 0
	if z <= -2.8e+110:
		tmp = (t - a) / (b - y)
	elif z <= 4e+85:
		tmp = ((z / t_1) * (t - a)) - (-x * (y / t_1))
	else:
		tmp = (t / (b - y)) - (a / (b - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(b - y) * z) + y)
	tmp = 0.0
	if (z <= -2.8e+110)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	elseif (z <= 4e+85)
		tmp = Float64(Float64(Float64(z / t_1) * Float64(t - a)) - Float64(Float64(-x) * Float64(y / t_1)));
	else
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((b - y) * z) + y;
	tmp = 0.0;
	if (z <= -2.8e+110)
		tmp = (t - a) / (b - y);
	elseif (z <= 4e+85)
		tmp = ((z / t_1) * (t - a)) - (-x * (y / t_1));
	else
		tmp = (t / (b - y)) - (a / (b - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(b - y), $MachinePrecision] * z), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[z, -2.8e+110], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+85], N[(N[(N[(z / t$95$1), $MachinePrecision] * N[(t - a), $MachinePrecision]), $MachinePrecision] - N[((-x) * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7999999999999999e110

   1. Initial program 66.8%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 50.9%

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

   4. Applied rewrites 50.9%

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

   if -2.7999999999999999e110 < z < 4.0000000000000001e85

   1. Initial program 66.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower--.f64 N/A

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

   3. Applied rewrites 79.4%

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

   if 4.0000000000000001e85 < z

   1. Initial program 66.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower--.f64 N/A

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

   3. Applied rewrites 79.4%

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

   4. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \frac{t}{b - y} - \frac{a}{b - y} \]

      4. lower-/.f64 N/A

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

      5. lower--.f64 50.5%

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

   6. Applied rewrites 50.5%

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

Alternative 7: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+25}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+52}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (if (<= z -1.85e+25)
  (/ (- t a) (- b y))
  (if (<= z 3.8e+52)
    (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))
    (- (/ t (- b y)) (/ a (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.85e+25) {
		tmp = (t - a) / (b - y);
	} else if (z <= 3.8e+52) {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	} else {
		tmp = (t / (b - y)) - (a / (b - 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, b)
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), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.85d+25)) then
        tmp = (t - a) / (b - y)
    else if (z <= 3.8d+52) then
        tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
    else
        tmp = (t / (b - y)) - (a / (b - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.85e+25) {
		tmp = (t - a) / (b - y);
	} else if (z <= 3.8e+52) {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	} else {
		tmp = (t / (b - y)) - (a / (b - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.85e+25:
		tmp = (t - a) / (b - y)
	elif z <= 3.8e+52:
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	else:
		tmp = (t / (b - y)) - (a / (b - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.85e+25)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	elseif (z <= 3.8e+52)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))));
	else
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.85e+25)
		tmp = (t - a) / (b - y);
	elseif (z <= 3.8e+52)
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	else
		tmp = (t / (b - y)) - (a / (b - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.85e+25], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+52], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8499999999999999e25

   1. Initial program 66.8%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 50.9%

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

   4. Applied rewrites 50.9%

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

   if -1.8499999999999999e25 < z < 3.8e52

   1. Initial program 66.8%

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

   if 3.8e52 < z

   1. Initial program 66.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower--.f64 N/A

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

   3. Applied rewrites 79.4%

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

   4. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \frac{t}{b - y} - \frac{a}{b - y} \]

      4. lower-/.f64 N/A

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

      5. lower--.f64 50.5%

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

   6. Applied rewrites 50.5%

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

Alternative 8: 83.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{-6}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 860000:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (if (<= z -1.22e-6)
  (/ (- t a) (- b y))
  (if (<= z 860000.0)
    (/ (+ (* x y) (* z (- t a))) (+ y (* z b)))
    (- (/ t (- b y)) (/ a (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.22e-6) {
		tmp = (t - a) / (b - y);
	} else if (z <= 860000.0) {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * b));
	} else {
		tmp = (t / (b - y)) - (a / (b - 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, b)
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), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.22d-6)) then
        tmp = (t - a) / (b - y)
    else if (z <= 860000.0d0) then
        tmp = ((x * y) + (z * (t - a))) / (y + (z * b))
    else
        tmp = (t / (b - y)) - (a / (b - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.22e-6) {
		tmp = (t - a) / (b - y);
	} else if (z <= 860000.0) {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * b));
	} else {
		tmp = (t / (b - y)) - (a / (b - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.22e-6:
		tmp = (t - a) / (b - y)
	elif z <= 860000.0:
		tmp = ((x * y) + (z * (t - a))) / (y + (z * b))
	else:
		tmp = (t / (b - y)) - (a / (b - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.22e-6)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	elseif (z <= 860000.0)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * b)));
	else
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.22e-6)
		tmp = (t - a) / (b - y);
	elseif (z <= 860000.0)
		tmp = ((x * y) + (z * (t - a))) / (y + (z * b));
	else
		tmp = (t / (b - y)) - (a / (b - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.22e-6], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 860000.0], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.22e-6

   1. Initial program 66.8%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 50.9%

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

   4. Applied rewrites 50.9%

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

   if -1.22e-6 < z < 8.6e5

   1. Initial program 66.8%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 57.5%

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

   if 8.6e5 < z

   1. Initial program 66.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower--.f64 N/A

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

   3. Applied rewrites 79.4%

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

   4. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \frac{t}{b - y} - \frac{a}{b - y} \]

      4. lower-/.f64 N/A

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

      5. lower--.f64 50.5%

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

   6. Applied rewrites 50.5%

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

Alternative 9: 71.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{-7}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-151}:\\ \;\;\;\;\frac{x \cdot y + t \cdot z}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-170}:\\ \;\;\;\;\frac{x}{\frac{\left(b - y\right) \cdot z + y}{y}}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-81}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{\left(1 - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (if (<= z -5.7e-7)
  (/ (- t a) (- b y))
  (if (<= z -3.6e-151)
    (/ (+ (* x y) (* t z)) (+ y (* z (- b y))))
    (if (<= z 2.5e-170)
      (/ x (/ (+ (* (- b y) z) y) y))
      (if (<= z 1.9e-81)
        (/ (+ (* x y) (* z (- t a))) (* (- 1.0 z) y))
        (- (/ t (- b y)) (/ a (- b y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.7e-7) {
		tmp = (t - a) / (b - y);
	} else if (z <= -3.6e-151) {
		tmp = ((x * y) + (t * z)) / (y + (z * (b - y)));
	} else if (z <= 2.5e-170) {
		tmp = x / ((((b - y) * z) + y) / y);
	} else if (z <= 1.9e-81) {
		tmp = ((x * y) + (z * (t - a))) / ((1.0 - z) * y);
	} else {
		tmp = (t / (b - y)) - (a / (b - 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, b)
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), intent (in) :: b
    real(8) :: tmp
    if (z <= (-5.7d-7)) then
        tmp = (t - a) / (b - y)
    else if (z <= (-3.6d-151)) then
        tmp = ((x * y) + (t * z)) / (y + (z * (b - y)))
    else if (z <= 2.5d-170) then
        tmp = x / ((((b - y) * z) + y) / y)
    else if (z <= 1.9d-81) then
        tmp = ((x * y) + (z * (t - a))) / ((1.0d0 - z) * y)
    else
        tmp = (t / (b - y)) - (a / (b - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.7e-7) {
		tmp = (t - a) / (b - y);
	} else if (z <= -3.6e-151) {
		tmp = ((x * y) + (t * z)) / (y + (z * (b - y)));
	} else if (z <= 2.5e-170) {
		tmp = x / ((((b - y) * z) + y) / y);
	} else if (z <= 1.9e-81) {
		tmp = ((x * y) + (z * (t - a))) / ((1.0 - z) * y);
	} else {
		tmp = (t / (b - y)) - (a / (b - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -5.7e-7:
		tmp = (t - a) / (b - y)
	elif z <= -3.6e-151:
		tmp = ((x * y) + (t * z)) / (y + (z * (b - y)))
	elif z <= 2.5e-170:
		tmp = x / ((((b - y) * z) + y) / y)
	elif z <= 1.9e-81:
		tmp = ((x * y) + (z * (t - a))) / ((1.0 - z) * y)
	else:
		tmp = (t / (b - y)) - (a / (b - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5.7e-7)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	elseif (z <= -3.6e-151)
		tmp = Float64(Float64(Float64(x * y) + Float64(t * z)) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 2.5e-170)
		tmp = Float64(x / Float64(Float64(Float64(Float64(b - y) * z) + y) / y));
	elseif (z <= 1.9e-81)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(Float64(1.0 - z) * y));
	else
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -5.7e-7)
		tmp = (t - a) / (b - y);
	elseif (z <= -3.6e-151)
		tmp = ((x * y) + (t * z)) / (y + (z * (b - y)));
	elseif (z <= 2.5e-170)
		tmp = x / ((((b - y) * z) + y) / y);
	elseif (z <= 1.9e-81)
		tmp = ((x * y) + (z * (t - a))) / ((1.0 - z) * y);
	else
		tmp = (t / (b - y)) - (a / (b - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5.7e-7], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.6e-151], N[(N[(N[(x * y), $MachinePrecision] + N[(t * z), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-170], N[(x / N[(N[(N[(N[(b - y), $MachinePrecision] * z), $MachinePrecision] + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-81], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.7000000000000005e-7

   1. Initial program 66.8%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 50.9%

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

   4. Applied rewrites 50.9%

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

   if -5.7000000000000005e-7 < z < -3.6000000000000003e-151

   1. Initial program 66.8%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 47.9%

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

   4. Applied rewrites 47.9%

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

   if -3.6000000000000003e-151 < z < 2.5000000000000001e-170

   1. Initial program 66.8%

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

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 29.3%

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

   4. Applied rewrites 29.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-+.f64 N/A

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

      10. div-flip-rev N/A

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

      11. lift-+.f64 N/A

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

      12. +-commutative N/A

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

      13. *-lft-identity N/A

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

      14. lift-*.f64 N/A

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

      15. fp-cancel-sign-sub N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lift--.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. sub-to-fraction N/A

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

      21. lift-/.f64 N/A

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

      22. lift--.f64 N/A

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

   6. Applied rewrites 36.5%

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

   if 2.5000000000000001e-170 < z < 1.8999999999999999e-81

   1. Initial program 66.8%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. sub-to-mult N/A

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

      4. lower-unsound-*.f64 N/A

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

      5. lower-unsound--.f64 N/A

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

      6. lower-unsound-/.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 61.0%

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

   3. Applied rewrites 61.0%

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

   4. Taylor expanded in y around inf

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

   6. Applied rewrites 42.8%

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

   if 1.8999999999999999e-81 < z

   1. Initial program 66.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower--.f64 N/A

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

   3. Applied rewrites 79.4%

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

   4. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \frac{t}{b - y} - \frac{a}{b - y} \]

      4. lower-/.f64 N/A

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

      5. lower--.f64 50.5%

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

   6. Applied rewrites 50.5%

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

Alternative 10: 71.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -5.7 \cdot 10^{-7}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-151}:\\ \;\;\;\;\frac{x \cdot y + t \cdot z}{t\_1}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-96}:\\ \;\;\;\;\frac{x}{\frac{\left(b - y\right) \cdot z + y}{y}}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+28}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (+ y (* z (- b y)))))
  (if (<= z -5.7e-7)
    (/ (- t a) (- b y))
    (if (<= z -3.6e-151)
      (/ (+ (* x y) (* t z)) t_1)
      (if (<= z 3.5e-96)
        (/ x (/ (+ (* (- b y) z) y) y))
        (if (<= z 9.8e+28)
          (/ (* z (- t a)) t_1)
          (- (/ t (- b y)) (/ a (- b y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if (z <= -5.7e-7) {
		tmp = (t - a) / (b - y);
	} else if (z <= -3.6e-151) {
		tmp = ((x * y) + (t * z)) / t_1;
	} else if (z <= 3.5e-96) {
		tmp = x / ((((b - y) * z) + y) / y);
	} else if (z <= 9.8e+28) {
		tmp = (z * (t - a)) / t_1;
	} else {
		tmp = (t / (b - y)) - (a / (b - 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, b)
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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    if (z <= (-5.7d-7)) then
        tmp = (t - a) / (b - y)
    else if (z <= (-3.6d-151)) then
        tmp = ((x * y) + (t * z)) / t_1
    else if (z <= 3.5d-96) then
        tmp = x / ((((b - y) * z) + y) / y)
    else if (z <= 9.8d+28) then
        tmp = (z * (t - a)) / t_1
    else
        tmp = (t / (b - y)) - (a / (b - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if (z <= -5.7e-7) {
		tmp = (t - a) / (b - y);
	} else if (z <= -3.6e-151) {
		tmp = ((x * y) + (t * z)) / t_1;
	} else if (z <= 3.5e-96) {
		tmp = x / ((((b - y) * z) + y) / y);
	} else if (z <= 9.8e+28) {
		tmp = (z * (t - a)) / t_1;
	} else {
		tmp = (t / (b - y)) - (a / (b - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if z <= -5.7e-7:
		tmp = (t - a) / (b - y)
	elif z <= -3.6e-151:
		tmp = ((x * y) + (t * z)) / t_1
	elif z <= 3.5e-96:
		tmp = x / ((((b - y) * z) + y) / y)
	elif z <= 9.8e+28:
		tmp = (z * (t - a)) / t_1
	else:
		tmp = (t / (b - y)) - (a / (b - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if (z <= -5.7e-7)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	elseif (z <= -3.6e-151)
		tmp = Float64(Float64(Float64(x * y) + Float64(t * z)) / t_1);
	elseif (z <= 3.5e-96)
		tmp = Float64(x / Float64(Float64(Float64(Float64(b - y) * z) + y) / y));
	elseif (z <= 9.8e+28)
		tmp = Float64(Float64(z * Float64(t - a)) / t_1);
	else
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	tmp = 0.0;
	if (z <= -5.7e-7)
		tmp = (t - a) / (b - y);
	elseif (z <= -3.6e-151)
		tmp = ((x * y) + (t * z)) / t_1;
	elseif (z <= 3.5e-96)
		tmp = x / ((((b - y) * z) + y) / y);
	elseif (z <= 9.8e+28)
		tmp = (z * (t - a)) / t_1;
	else
		tmp = (t / (b - y)) - (a / (b - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.7e-7], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.6e-151], N[(N[(N[(x * y), $MachinePrecision] + N[(t * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 3.5e-96], N[(x / N[(N[(N[(N[(b - y), $MachinePrecision] * z), $MachinePrecision] + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e+28], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.7000000000000005e-7

   1. Initial program 66.8%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 50.9%

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

   4. Applied rewrites 50.9%

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

   if -5.7000000000000005e-7 < z < -3.6000000000000003e-151

   1. Initial program 66.8%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 47.9%

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

   4. Applied rewrites 47.9%

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

   if -3.6000000000000003e-151 < z < 3.4999999999999999e-96

   1. Initial program 66.8%

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

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 29.3%

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

   4. Applied rewrites 29.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-+.f64 N/A

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

      10. div-flip-rev N/A

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

      11. lift-+.f64 N/A

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

      12. +-commutative N/A

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

      13. *-lft-identity N/A

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

      14. lift-*.f64 N/A

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

      15. fp-cancel-sign-sub N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lift--.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. sub-to-fraction N/A

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

      21. lift-/.f64 N/A

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

      22. lift--.f64 N/A

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

   6. Applied rewrites 36.5%

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

   if 3.4999999999999999e-96 < z < 9.7999999999999992e28

   1. Initial program 66.8%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 41.6%

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

   4. Applied rewrites 41.6%

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

   if 9.7999999999999992e28 < z

   1. Initial program 66.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower--.f64 N/A

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

   3. Applied rewrites 79.4%

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

   4. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \frac{t}{b - y} - \frac{a}{b - y} \]

      4. lower-/.f64 N/A

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

      5. lower--.f64 50.5%

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

   6. Applied rewrites 50.5%

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

Alternative 11: 71.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+14}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-151}:\\ \;\;\;\;\frac{x \cdot y + t \cdot z}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-96}:\\ \;\;\;\;\frac{x}{\frac{\left(b - y\right) \cdot z + y}{y}}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+28}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (if (<= z -4.6e+14)
  (/ (- t a) (- b y))
  (if (<= z -3.6e-151)
    (/ (+ (* x y) (* t z)) (+ y (* z b)))
    (if (<= z 3.5e-96)
      (/ x (/ (+ (* (- b y) z) y) y))
      (if (<= z 9.8e+28)
        (/ (* z (- t a)) (+ y (* z (- b y))))
        (- (/ t (- b y)) (/ a (- b y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.6e+14) {
		tmp = (t - a) / (b - y);
	} else if (z <= -3.6e-151) {
		tmp = ((x * y) + (t * z)) / (y + (z * b));
	} else if (z <= 3.5e-96) {
		tmp = x / ((((b - y) * z) + y) / y);
	} else if (z <= 9.8e+28) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else {
		tmp = (t / (b - y)) - (a / (b - 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, b)
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), intent (in) :: b
    real(8) :: tmp
    if (z <= (-4.6d+14)) then
        tmp = (t - a) / (b - y)
    else if (z <= (-3.6d-151)) then
        tmp = ((x * y) + (t * z)) / (y + (z * b))
    else if (z <= 3.5d-96) then
        tmp = x / ((((b - y) * z) + y) / y)
    else if (z <= 9.8d+28) then
        tmp = (z * (t - a)) / (y + (z * (b - y)))
    else
        tmp = (t / (b - y)) - (a / (b - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.6e+14) {
		tmp = (t - a) / (b - y);
	} else if (z <= -3.6e-151) {
		tmp = ((x * y) + (t * z)) / (y + (z * b));
	} else if (z <= 3.5e-96) {
		tmp = x / ((((b - y) * z) + y) / y);
	} else if (z <= 9.8e+28) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else {
		tmp = (t / (b - y)) - (a / (b - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.6e+14:
		tmp = (t - a) / (b - y)
	elif z <= -3.6e-151:
		tmp = ((x * y) + (t * z)) / (y + (z * b))
	elif z <= 3.5e-96:
		tmp = x / ((((b - y) * z) + y) / y)
	elif z <= 9.8e+28:
		tmp = (z * (t - a)) / (y + (z * (b - y)))
	else:
		tmp = (t / (b - y)) - (a / (b - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.6e+14)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	elseif (z <= -3.6e-151)
		tmp = Float64(Float64(Float64(x * y) + Float64(t * z)) / Float64(y + Float64(z * b)));
	elseif (z <= 3.5e-96)
		tmp = Float64(x / Float64(Float64(Float64(Float64(b - y) * z) + y) / y));
	elseif (z <= 9.8e+28)
		tmp = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y))));
	else
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4.6e+14)
		tmp = (t - a) / (b - y);
	elseif (z <= -3.6e-151)
		tmp = ((x * y) + (t * z)) / (y + (z * b));
	elseif (z <= 3.5e-96)
		tmp = x / ((((b - y) * z) + y) / y);
	elseif (z <= 9.8e+28)
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	else
		tmp = (t / (b - y)) - (a / (b - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.6e+14], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.6e-151], N[(N[(N[(x * y), $MachinePrecision] + N[(t * z), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-96], N[(x / N[(N[(N[(N[(b - y), $MachinePrecision] * z), $MachinePrecision] + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e+28], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.6e14

   1. Initial program 66.8%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 50.9%

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

   4. Applied rewrites 50.9%

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

   if -4.6e14 < z < -3.6000000000000003e-151

   1. Initial program 66.8%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 57.5%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 42.0%

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

   7. Applied rewrites 42.0%

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

   if -3.6000000000000003e-151 < z < 3.4999999999999999e-96

   1. Initial program 66.8%

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

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 29.3%

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

   4. Applied rewrites 29.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-+.f64 N/A

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

      10. div-flip-rev N/A

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

      11. lift-+.f64 N/A

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

      12. +-commutative N/A

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

      13. *-lft-identity N/A

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

      14. lift-*.f64 N/A

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

      15. fp-cancel-sign-sub N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lift--.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. sub-to-fraction N/A

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

      21. lift-/.f64 N/A

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

      22. lift--.f64 N/A

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

   6. Applied rewrites 36.5%

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

   if 3.4999999999999999e-96 < z < 9.7999999999999992e28

   1. Initial program 66.8%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 41.6%

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

   4. Applied rewrites 41.6%

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

   if 9.7999999999999992e28 < z

   1. Initial program 66.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower--.f64 N/A

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

   3. Applied rewrites 79.4%

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

   4. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \frac{t}{b - y} - \frac{a}{b - y} \]

      4. lower-/.f64 N/A

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

      5. lower--.f64 50.5%

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

   6. Applied rewrites 50.5%

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

Alternative 12: 70.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+14}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-151}:\\ \;\;\;\;\frac{x \cdot y + t \cdot z}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-96}:\\ \;\;\;\;\frac{y}{\left(b - y\right) \cdot z + y} \cdot x\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+28}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (if (<= z -4.6e+14)
  (/ (- t a) (- b y))
  (if (<= z -3.6e-151)
    (/ (+ (* x y) (* t z)) (+ y (* z b)))
    (if (<= z 3.5e-96)
      (* (/ y (+ (* (- b y) z) y)) x)
      (if (<= z 9.8e+28)
        (/ (* z (- t a)) (+ y (* z (- b y))))
        (- (/ t (- b y)) (/ a (- b y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.6e+14) {
		tmp = (t - a) / (b - y);
	} else if (z <= -3.6e-151) {
		tmp = ((x * y) + (t * z)) / (y + (z * b));
	} else if (z <= 3.5e-96) {
		tmp = (y / (((b - y) * z) + y)) * x;
	} else if (z <= 9.8e+28) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else {
		tmp = (t / (b - y)) - (a / (b - 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, b)
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), intent (in) :: b
    real(8) :: tmp
    if (z <= (-4.6d+14)) then
        tmp = (t - a) / (b - y)
    else if (z <= (-3.6d-151)) then
        tmp = ((x * y) + (t * z)) / (y + (z * b))
    else if (z <= 3.5d-96) then
        tmp = (y / (((b - y) * z) + y)) * x
    else if (z <= 9.8d+28) then
        tmp = (z * (t - a)) / (y + (z * (b - y)))
    else
        tmp = (t / (b - y)) - (a / (b - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.6e+14) {
		tmp = (t - a) / (b - y);
	} else if (z <= -3.6e-151) {
		tmp = ((x * y) + (t * z)) / (y + (z * b));
	} else if (z <= 3.5e-96) {
		tmp = (y / (((b - y) * z) + y)) * x;
	} else if (z <= 9.8e+28) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else {
		tmp = (t / (b - y)) - (a / (b - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.6e+14:
		tmp = (t - a) / (b - y)
	elif z <= -3.6e-151:
		tmp = ((x * y) + (t * z)) / (y + (z * b))
	elif z <= 3.5e-96:
		tmp = (y / (((b - y) * z) + y)) * x
	elif z <= 9.8e+28:
		tmp = (z * (t - a)) / (y + (z * (b - y)))
	else:
		tmp = (t / (b - y)) - (a / (b - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.6e+14)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	elseif (z <= -3.6e-151)
		tmp = Float64(Float64(Float64(x * y) + Float64(t * z)) / Float64(y + Float64(z * b)));
	elseif (z <= 3.5e-96)
		tmp = Float64(Float64(y / Float64(Float64(Float64(b - y) * z) + y)) * x);
	elseif (z <= 9.8e+28)
		tmp = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y))));
	else
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4.6e+14)
		tmp = (t - a) / (b - y);
	elseif (z <= -3.6e-151)
		tmp = ((x * y) + (t * z)) / (y + (z * b));
	elseif (z <= 3.5e-96)
		tmp = (y / (((b - y) * z) + y)) * x;
	elseif (z <= 9.8e+28)
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	else
		tmp = (t / (b - y)) - (a / (b - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.6e+14], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.6e-151], N[(N[(N[(x * y), $MachinePrecision] + N[(t * z), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-96], N[(N[(y / N[(N[(N[(b - y), $MachinePrecision] * z), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 9.8e+28], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.6e14

   1. Initial program 66.8%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 50.9%

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

   4. Applied rewrites 50.9%

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

   if -4.6e14 < z < -3.6000000000000003e-151

   1. Initial program 66.8%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 57.5%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 42.0%

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

   7. Applied rewrites 42.0%

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

   if -3.6000000000000003e-151 < z < 3.4999999999999999e-96

   1. Initial program 66.8%

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

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 29.3%

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

   4. Applied rewrites 29.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-+.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. *-commutative N/A

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

   6. Applied rewrites 36.5%

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

   if 3.4999999999999999e-96 < z < 9.7999999999999992e28

   1. Initial program 66.8%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 41.6%

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

   4. Applied rewrites 41.6%

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

   if 9.7999999999999992e28 < z

   1. Initial program 66.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower--.f64 N/A

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

   3. Applied rewrites 79.4%

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

   4. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \frac{t}{b - y} - \frac{a}{b - y} \]

      4. lower-/.f64 N/A

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

      5. lower--.f64 50.5%

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

   6. Applied rewrites 50.5%

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

Alternative 13: 70.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-28}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-96}:\\ \;\;\;\;\frac{y}{\left(b - y\right) \cdot z + y} \cdot x\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+28}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (if (<= z -9.5e-28)
  (/ (- t a) (- b y))
  (if (<= z 3.5e-96)
    (* (/ y (+ (* (- b y) z) y)) x)
    (if (<= z 9.8e+28)
      (/ (* z (- t a)) (+ y (* z (- b y))))
      (- (/ t (- b y)) (/ a (- b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -9.5e-28) {
		tmp = (t - a) / (b - y);
	} else if (z <= 3.5e-96) {
		tmp = (y / (((b - y) * z) + y)) * x;
	} else if (z <= 9.8e+28) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else {
		tmp = (t / (b - y)) - (a / (b - 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, b)
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), intent (in) :: b
    real(8) :: tmp
    if (z <= (-9.5d-28)) then
        tmp = (t - a) / (b - y)
    else if (z <= 3.5d-96) then
        tmp = (y / (((b - y) * z) + y)) * x
    else if (z <= 9.8d+28) then
        tmp = (z * (t - a)) / (y + (z * (b - y)))
    else
        tmp = (t / (b - y)) - (a / (b - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -9.5e-28) {
		tmp = (t - a) / (b - y);
	} else if (z <= 3.5e-96) {
		tmp = (y / (((b - y) * z) + y)) * x;
	} else if (z <= 9.8e+28) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else {
		tmp = (t / (b - y)) - (a / (b - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -9.5e-28:
		tmp = (t - a) / (b - y)
	elif z <= 3.5e-96:
		tmp = (y / (((b - y) * z) + y)) * x
	elif z <= 9.8e+28:
		tmp = (z * (t - a)) / (y + (z * (b - y)))
	else:
		tmp = (t / (b - y)) - (a / (b - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -9.5e-28)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	elseif (z <= 3.5e-96)
		tmp = Float64(Float64(y / Float64(Float64(Float64(b - y) * z) + y)) * x);
	elseif (z <= 9.8e+28)
		tmp = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y))));
	else
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -9.5e-28)
		tmp = (t - a) / (b - y);
	elseif (z <= 3.5e-96)
		tmp = (y / (((b - y) * z) + y)) * x;
	elseif (z <= 9.8e+28)
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	else
		tmp = (t / (b - y)) - (a / (b - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -9.5e-28], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-96], N[(N[(y / N[(N[(N[(b - y), $MachinePrecision] * z), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 9.8e+28], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.5e-28

   1. Initial program 66.8%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 50.9%

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

   4. Applied rewrites 50.9%

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

   if -9.5e-28 < z < 3.4999999999999999e-96

   1. Initial program 66.8%

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

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 29.3%

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

   4. Applied rewrites 29.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-+.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. *-commutative N/A

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

   6. Applied rewrites 36.5%

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

   if 3.4999999999999999e-96 < z < 9.7999999999999992e28

   1. Initial program 66.8%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 41.6%

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

   4. Applied rewrites 41.6%

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

   if 9.7999999999999992e28 < z

   1. Initial program 66.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

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

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

      8. lower--.f64 N/A

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

   3. Applied rewrites 79.4%

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

   4. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \frac{t}{b - y} - \frac{a}{b - y} \]

      4. lower-/.f64 N/A

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

      5. lower--.f64 50.5%

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

   6. Applied rewrites 50.5%

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

Alternative 14: 69.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-96}:\\ \;\;\;\;\frac{y}{\left(b - y\right) \cdot z + y} \cdot x\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+28}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (/ (- t a) (- b y))))
  (if (<= z -9.5e-28)
    t_1
    (if (<= z 3.5e-96)
      (* (/ y (+ (* (- b y) z) y)) x)
      (if (<= z 9.8e+28) (/ (* z (- t a)) (+ y (* z (- b y)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -9.5e-28) {
		tmp = t_1;
	} else if (z <= 3.5e-96) {
		tmp = (y / (((b - y) * z) + y)) * x;
	} else if (z <= 9.8e+28) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} 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, b)
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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-9.5d-28)) then
        tmp = t_1
    else if (z <= 3.5d-96) then
        tmp = (y / (((b - y) * z) + y)) * x
    else if (z <= 9.8d+28) then
        tmp = (z * (t - a)) / (y + (z * (b - y)))
    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 b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -9.5e-28) {
		tmp = t_1;
	} else if (z <= 3.5e-96) {
		tmp = (y / (((b - y) * z) + y)) * x;
	} else if (z <= 9.8e+28) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -9.5e-28:
		tmp = t_1
	elif z <= 3.5e-96:
		tmp = (y / (((b - y) * z) + y)) * x
	elif z <= 9.8e+28:
		tmp = (z * (t - a)) / (y + (z * (b - y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -9.5e-28)
		tmp = t_1;
	elseif (z <= 3.5e-96)
		tmp = Float64(Float64(y / Float64(Float64(Float64(b - y) * z) + y)) * x);
	elseif (z <= 9.8e+28)
		tmp = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -9.5e-28)
		tmp = t_1;
	elseif (z <= 3.5e-96)
		tmp = (y / (((b - y) * z) + y)) * x;
	elseif (z <= 9.8e+28)
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e-28], t$95$1, If[LessEqual[z, 3.5e-96], N[(N[(y / N[(N[(N[(b - y), $MachinePrecision] * z), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 9.8e+28], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5e-28 or 9.7999999999999992e28 < z

   1. Initial program 66.8%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 50.9%

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

   4. Applied rewrites 50.9%

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

   if -9.5e-28 < z < 3.4999999999999999e-96

   1. Initial program 66.8%

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

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 29.3%

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

   4. Applied rewrites 29.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-+.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. *-commutative N/A

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

   6. Applied rewrites 36.5%

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

   if 3.4999999999999999e-96 < z < 9.7999999999999992e28

   1. Initial program 66.8%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 41.6%

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

   4. Applied rewrites 41.6%

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

Alternative 15: 69.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-96}:\\ \;\;\;\;\frac{y}{\left(b - y\right) \cdot z + y} \cdot x\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-11}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (/ (- t a) (- b y))))
  (if (<= z -9.5e-28)
    t_1
    (if (<= z 3.5e-96)
      (* (/ y (+ (* (- b y) z) y)) x)
      (if (<= z 1.18e-11) (/ (* z (- t a)) (+ y (* z b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -9.5e-28) {
		tmp = t_1;
	} else if (z <= 3.5e-96) {
		tmp = (y / (((b - y) * z) + y)) * x;
	} else if (z <= 1.18e-11) {
		tmp = (z * (t - a)) / (y + (z * b));
	} 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, b)
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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-9.5d-28)) then
        tmp = t_1
    else if (z <= 3.5d-96) then
        tmp = (y / (((b - y) * z) + y)) * x
    else if (z <= 1.18d-11) then
        tmp = (z * (t - a)) / (y + (z * b))
    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 b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -9.5e-28) {
		tmp = t_1;
	} else if (z <= 3.5e-96) {
		tmp = (y / (((b - y) * z) + y)) * x;
	} else if (z <= 1.18e-11) {
		tmp = (z * (t - a)) / (y + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -9.5e-28:
		tmp = t_1
	elif z <= 3.5e-96:
		tmp = (y / (((b - y) * z) + y)) * x
	elif z <= 1.18e-11:
		tmp = (z * (t - a)) / (y + (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -9.5e-28)
		tmp = t_1;
	elseif (z <= 3.5e-96)
		tmp = Float64(Float64(y / Float64(Float64(Float64(b - y) * z) + y)) * x);
	elseif (z <= 1.18e-11)
		tmp = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -9.5e-28)
		tmp = t_1;
	elseif (z <= 3.5e-96)
		tmp = (y / (((b - y) * z) + y)) * x;
	elseif (z <= 1.18e-11)
		tmp = (z * (t - a)) / (y + (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e-28], t$95$1, If[LessEqual[z, 3.5e-96], N[(N[(y / N[(N[(N[(b - y), $MachinePrecision] * z), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 1.18e-11], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5e-28 or 1.1800000000000001e-11 < z

   1. Initial program 66.8%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 50.9%

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

   4. Applied rewrites 50.9%

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

   if -9.5e-28 < z < 3.4999999999999999e-96

   1. Initial program 66.8%

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

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 29.3%

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

   4. Applied rewrites 29.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-+.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. *-commutative N/A

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

   6. Applied rewrites 36.5%

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

   if 3.4999999999999999e-96 < z < 1.1800000000000001e-11

   1. Initial program 66.8%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 57.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 34.9%

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

   7. Applied rewrites 34.9%

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

Alternative 16: 68.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-48}:\\ \;\;\;\;\frac{y}{\left(b - y\right) \cdot z + y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (/ (- t a) (- b y))))
  (if (<= z -9.5e-28)
    t_1
    (if (<= z 1.85e-48) (* (/ y (+ (* (- b y) z) y)) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -9.5e-28) {
		tmp = t_1;
	} else if (z <= 1.85e-48) {
		tmp = (y / (((b - y) * z) + y)) * 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, b)
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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-9.5d-28)) then
        tmp = t_1
    else if (z <= 1.85d-48) then
        tmp = (y / (((b - y) * z) + y)) * 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 b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -9.5e-28) {
		tmp = t_1;
	} else if (z <= 1.85e-48) {
		tmp = (y / (((b - y) * z) + y)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -9.5e-28:
		tmp = t_1
	elif z <= 1.85e-48:
		tmp = (y / (((b - y) * z) + y)) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -9.5e-28)
		tmp = t_1;
	elseif (z <= 1.85e-48)
		tmp = Float64(Float64(y / Float64(Float64(Float64(b - y) * z) + y)) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -9.5e-28)
		tmp = t_1;
	elseif (z <= 1.85e-48)
		tmp = (y / (((b - y) * z) + y)) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e-28], t$95$1, If[LessEqual[z, 1.85e-48], N[(N[(y / N[(N[(N[(b - y), $MachinePrecision] * z), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5e-28 or 1.8499999999999999e-48 < z

   1. Initial program 66.8%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 50.9%

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

   4. Applied rewrites 50.9%

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

   if -9.5e-28 < z < 1.8499999999999999e-48

   1. Initial program 66.8%

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

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 29.3%

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

   4. Applied rewrites 29.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-+.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. *-commutative N/A

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

   6. Applied rewrites 36.5%

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

Alternative 17: 64.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-81}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (/ (- t a) (- b y))))
  (if (<= z -6.6e-79) t_1 (if (<= z 1.9e-81) (+ x (* x z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -6.6e-79) {
		tmp = t_1;
	} else if (z <= 1.9e-81) {
		tmp = x + (x * z);
	} 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, b)
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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-6.6d-79)) then
        tmp = t_1
    else if (z <= 1.9d-81) then
        tmp = x + (x * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -6.6e-79) {
		tmp = t_1;
	} else if (z <= 1.9e-81) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -6.6e-79:
		tmp = t_1
	elif z <= 1.9e-81:
		tmp = x + (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -6.6e-79)
		tmp = t_1;
	elseif (z <= 1.9e-81)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -6.6e-79)
		tmp = t_1;
	elseif (z <= 1.9e-81)
		tmp = x + (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.6e-79], t$95$1, If[LessEqual[z, 1.9e-81], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5999999999999996e-79 or 1.8999999999999999e-81 < z

   1. Initial program 66.8%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 50.9%

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

   4. Applied rewrites 50.9%

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

   if -6.5999999999999996e-79 < z < 1.8999999999999999e-81

   1. Initial program 66.8%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. sub-to-mult N/A

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

      4. lower-unsound-*.f64 N/A

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

      5. lower-unsound--.f64 N/A

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

      6. lower-unsound-/.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 61.0%

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

   3. Applied rewrites 61.0%

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

   4. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

      2. lower--.f64 33.4%

         \[\leadsto \frac{x}{1 - \color{blue}{z}} \]

   6. Applied rewrites 33.4%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   7. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 25.8%

         \[\leadsto x + x \cdot z \]

   9. Applied rewrites 25.8%

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

Alternative 18: 53.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -4.7 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+65}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (/ x (- 1.0 z))))
  (if (<= y -4.7e+39) t_1 (if (<= y 3e+65) (/ (- t a) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -4.7e+39) {
		tmp = t_1;
	} else if (y <= 3e+65) {
		tmp = (t - a) / b;
	} 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, b)
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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-4.7d+39)) then
        tmp = t_1
    else if (y <= 3d+65) then
        tmp = (t - a) / b
    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 b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -4.7e+39) {
		tmp = t_1;
	} else if (y <= 3e+65) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -4.7e+39:
		tmp = t_1
	elif y <= 3e+65:
		tmp = (t - a) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -4.7e+39)
		tmp = t_1;
	elseif (y <= 3e+65)
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -4.7e+39)
		tmp = t_1;
	elseif (y <= 3e+65)
		tmp = (t - a) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.7e+39], t$95$1, If[LessEqual[y, 3e+65], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.6999999999999999e39 or 3.0000000000000002e65 < y

   1. Initial program 66.8%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. sub-to-mult N/A

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

      4. lower-unsound-*.f64 N/A

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

      5. lower-unsound--.f64 N/A

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

      6. lower-unsound-/.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 61.0%

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

   3. Applied rewrites 61.0%

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

   4. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

      2. lower--.f64 33.4%

         \[\leadsto \frac{x}{1 - \color{blue}{z}} \]

   6. Applied rewrites 33.4%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   if -4.6999999999999999e39 < y < 3.0000000000000002e65

   1. Initial program 66.8%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{t - a}{b}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower--.f64 34.7%

         \[\leadsto \frac{t - a}{b} \]

   4. Applied rewrites 34.7%

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

Alternative 19: 41.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -180000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-22}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (/ x (- 1.0 z))))
  (if (<= y -180000000000.0) t_1 (if (<= y 7.2e-22) (/ t b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -180000000000.0) {
		tmp = t_1;
	} else if (y <= 7.2e-22) {
		tmp = t / b;
	} 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, b)
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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-180000000000.0d0)) then
        tmp = t_1
    else if (y <= 7.2d-22) then
        tmp = t / b
    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 b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -180000000000.0) {
		tmp = t_1;
	} else if (y <= 7.2e-22) {
		tmp = t / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -180000000000.0:
		tmp = t_1
	elif y <= 7.2e-22:
		tmp = t / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -180000000000.0)
		tmp = t_1;
	elseif (y <= 7.2e-22)
		tmp = Float64(t / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -180000000000.0)
		tmp = t_1;
	elseif (y <= 7.2e-22)
		tmp = t / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -180000000000.0], t$95$1, If[LessEqual[y, 7.2e-22], N[(t / b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e11 or 7.1999999999999996e-22 < y

   1. Initial program 66.8%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. sub-to-mult N/A

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

      4. lower-unsound-*.f64 N/A

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

      5. lower-unsound--.f64 N/A

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

      6. lower-unsound-/.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 61.0%

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

   3. Applied rewrites 61.0%

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

   4. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

      2. lower--.f64 33.4%

         \[\leadsto \frac{x}{1 - \color{blue}{z}} \]

   6. Applied rewrites 33.4%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   if -1.8e11 < y < 7.1999999999999996e-22

   1. Initial program 66.8%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{t - a}{b}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower--.f64 34.7%

         \[\leadsto \frac{t - a}{b} \]

   4. Applied rewrites 34.7%

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

   5. Taylor expanded in t around inf

      \[\leadsto \frac{t}{\color{blue}{b}} \]
   6. Step-by-step derivation

      1. lower-/.f64 19.7%

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

   7. Applied rewrites 19.7%

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

Alternative 20: 35.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-77}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-91}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (if (<= z -6.2e-77) (/ t b) (if (<= z 5.5e-91) (+ x (* x z)) (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.2e-77) {
		tmp = t / b;
	} else if (z <= 5.5e-91) {
		tmp = x + (x * z);
	} else {
		tmp = t / b;
	}
	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, b)
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), intent (in) :: b
    real(8) :: tmp
    if (z <= (-6.2d-77)) then
        tmp = t / b
    else if (z <= 5.5d-91) then
        tmp = x + (x * z)
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.2e-77) {
		tmp = t / b;
	} else if (z <= 5.5e-91) {
		tmp = x + (x * z);
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6.2e-77:
		tmp = t / b
	elif z <= 5.5e-91:
		tmp = x + (x * z)
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6.2e-77)
		tmp = Float64(t / b);
	elseif (z <= 5.5e-91)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6.2e-77)
		tmp = t / b;
	elseif (z <= 5.5e-91)
		tmp = x + (x * z);
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6.2e-77], N[(t / b), $MachinePrecision], If[LessEqual[z, 5.5e-91], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2000000000000002e-77 or 5.4999999999999996e-91 < z

   1. Initial program 66.8%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{t - a}{b}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower--.f64 34.7%

         \[\leadsto \frac{t - a}{b} \]

   4. Applied rewrites 34.7%

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

   5. Taylor expanded in t around inf

      \[\leadsto \frac{t}{\color{blue}{b}} \]
   6. Step-by-step derivation

      1. lower-/.f64 19.7%

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

   7. Applied rewrites 19.7%

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

   if -6.2000000000000002e-77 < z < 5.4999999999999996e-91

   1. Initial program 66.8%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. sub-to-mult N/A

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

      4. lower-unsound-*.f64 N/A

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

      5. lower-unsound--.f64 N/A

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

      6. lower-unsound-/.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\left(1 - \frac{\mathsf{neg}\left(\color{blue}{\left(b - y\right) \cdot z}\right)}{y}\right) \cdot y} \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\left(1 - \frac{\color{blue}{\left(\mathsf{neg}\left(\left(b - y\right)\right)\right) \cdot z}}{y}\right) \cdot y} \]

      10. lift--.f64 N/A

          \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\left(1 - \frac{\left(\mathsf{neg}\left(\color{blue}{\left(b - y\right)}\right)\right) \cdot z}{y}\right) \cdot y} \]

      11. sub-negate-rev N/A

          \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\left(1 - \frac{\color{blue}{\left(y - b\right)} \cdot z}{y}\right) \cdot y} \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\left(1 - \frac{\color{blue}{\left(y - b\right) \cdot z}}{y}\right) \cdot y} \]

      13. lower--.f64 61.0%

          \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\left(1 - \frac{\color{blue}{\left(y - b\right)} \cdot z}{y}\right) \cdot y} \]

   3. Applied rewrites 61.0%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{\left(1 - \frac{\left(y - b\right) \cdot z}{y}\right) \cdot y}} \]

   4. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

      2. lower--.f64 33.4%

         \[\leadsto \frac{x}{1 - \color{blue}{z}} \]

   6. Applied rewrites 33.4%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   7. Taylor expanded in z around 0

      \[\leadsto x + \color{blue}{x \cdot z} \]
   8. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto x + x \cdot \color{blue}{z} \]

      2. lower-*.f64 25.8%

         \[\leadsto x + x \cdot z \]

   9. Applied rewrites 25.8%

      \[\leadsto x + \color{blue}{x \cdot z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 25.8% accurate, 4.3× speedup

Math

\[x + x \cdot z \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (+ x (* x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x + (x * z);
}

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, b)
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), intent (in) :: b
    code = x + (x * z)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x + (x * z);
}

Python

def code(x, y, z, t, a, b):
	return x + (x * z)

Julia

function code(x, y, z, t, a, b)
	return Float64(x + Float64(x * z))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x + (x * z);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 66.8%

   \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
2. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{y + z \cdot \left(b - y\right)}} \]

   2. add-flip N/A

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{y - \left(\mathsf{neg}\left(z \cdot \left(b - y\right)\right)\right)}} \]

   3. sub-to-mult N/A

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{\left(1 - \frac{\mathsf{neg}\left(z \cdot \left(b - y\right)\right)}{y}\right) \cdot y}} \]

   4. lower-unsound-*.f64 N/A

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{\left(1 - \frac{\mathsf{neg}\left(z \cdot \left(b - y\right)\right)}{y}\right) \cdot y}} \]

   5. lower-unsound--.f64 N/A

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{\left(1 - \frac{\mathsf{neg}\left(z \cdot \left(b - y\right)\right)}{y}\right)} \cdot y} \]

   6. lower-unsound-/.f64 N/A

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\left(1 - \color{blue}{\frac{\mathsf{neg}\left(z \cdot \left(b - y\right)\right)}{y}}\right) \cdot y} \]

   7. lift-*.f64 N/A

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\left(1 - \frac{\mathsf{neg}\left(\color{blue}{z \cdot \left(b - y\right)}\right)}{y}\right) \cdot y} \]

   8. *-commutative N/A

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\left(1 - \frac{\mathsf{neg}\left(\color{blue}{\left(b - y\right) \cdot z}\right)}{y}\right) \cdot y} \]

   9. distribute-lft-neg-in N/A

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\left(1 - \frac{\color{blue}{\left(\mathsf{neg}\left(\left(b - y\right)\right)\right) \cdot z}}{y}\right) \cdot y} \]

   10. lift--.f64 N/A

       \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\left(1 - \frac{\left(\mathsf{neg}\left(\color{blue}{\left(b - y\right)}\right)\right) \cdot z}{y}\right) \cdot y} \]

   11. sub-negate-rev N/A

       \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\left(1 - \frac{\color{blue}{\left(y - b\right)} \cdot z}{y}\right) \cdot y} \]

   12. lower-*.f64 N/A

       \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\left(1 - \frac{\color{blue}{\left(y - b\right) \cdot z}}{y}\right) \cdot y} \]

   13. lower--.f64 61.0%

       \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\left(1 - \frac{\color{blue}{\left(y - b\right)} \cdot z}{y}\right) \cdot y} \]

3. Applied rewrites 61.0%

   \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{\left(1 - \frac{\left(y - b\right) \cdot z}{y}\right) \cdot y}} \]

4. Taylor expanded in y around inf

   \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
5. Step-by-step derivation

   1. lower-/.f64 N/A

      \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   2. lower--.f64 33.4%

      \[\leadsto \frac{x}{1 - \color{blue}{z}} \]

6. Applied rewrites 33.4%

   \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

7. Taylor expanded in z around 0

   \[\leadsto x + \color{blue}{x \cdot z} \]
8. Step-by-step derivation

   1. lower-+.f64 N/A

      \[\leadsto x + x \cdot \color{blue}{z} \]

   2. lower-*.f64 25.8%

      \[\leadsto x + x \cdot z \]

9. Applied rewrites 25.8%

   \[\leadsto x + \color{blue}{x \cdot z} \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2025258 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64
  (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))