Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2

Percentage Accurate: 95.6% → 97.6%

Time: 5.2s

Alternatives: 22

Speedup: 1.1×

• 35.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

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 - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

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 - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (fma (- 1.0 y) z (- x (fma (- (- 2.0 y) t) b (* a (- t 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return fma((1.0 - y), z, (x - fma(((2.0 - y) - t), b, (a * (t - 1.0)))));
}

Julia

function code(x, y, z, t, a, b)
	return fma(Float64(1.0 - y), z, Float64(x - fma(Float64(Float64(2.0 - y) - t), b, Float64(a * Float64(t - 1.0)))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(1.0 - y), $MachinePrecision] * z + N[(x - N[(N[(N[(2.0 - y), $MachinePrecision] - t), $MachinePrecision] * b + N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.6%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. add-flip N/A

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

   3. lift--.f64 N/A

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

   4. sub-flip N/A

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

   5. associate--l+ N/A

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

   6. lift--.f64 N/A

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

   7. sub-flip N/A

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

   8. +-commutative N/A

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

   9. associate-+l+ N/A

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

   10. lift-*.f64 N/A

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

   11. distribute-lft-neg-out N/A

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

   12. lift--.f64 N/A

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

   13. sub-negate-rev N/A

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

   14. add-flip-rev N/A

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

   15. sub-negate-rev N/A

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

3. Applied rewrites 97.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]
4. Add Preprocessing

Alternative 2: 94.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - y, z, x - t \cdot \left(a + -1 \cdot b\right)\right)\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(-1, a, b \cdot \left(2 - y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 y) z (- x (* t (+ a (* -1.0 b)))))))
   (if (<= t -4.8e+45)
     t_1
     (if (<= t 1.45e-5)
       (fma (- 1.0 y) z (- x (fma -1.0 a (* b (- 2.0 y)))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - y), z, (x - (t * (a + (-1.0 * b)))));
	double tmp;
	if (t <= -4.8e+45) {
		tmp = t_1;
	} else if (t <= 1.45e-5) {
		tmp = fma((1.0 - y), z, (x - fma(-1.0, a, (b * (2.0 - y)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - y), z, Float64(x - Float64(t * Float64(a + Float64(-1.0 * b)))))
	tmp = 0.0
	if (t <= -4.8e+45)
		tmp = t_1;
	elseif (t <= 1.45e-5)
		tmp = fma(Float64(1.0 - y), z, Float64(x - fma(-1.0, a, Float64(b * Float64(2.0 - y)))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z + N[(x - N[(t * N[(a + N[(-1.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.8e+45], t$95$1, If[LessEqual[t, 1.45e-5], N[(N[(1.0 - y), $MachinePrecision] * z + N[(x - N[(-1.0 * a + N[(b * N[(2.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.79999999999999979e45 or 1.45e-5 < t

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 70.6

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

   6. Applied rewrites 70.6%

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

   if -4.79999999999999979e45 < t < 1.45e-5

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(1 - y, z, x - \color{blue}{\left(-1 \cdot a + b \cdot \left(2 - y\right)\right)}\right) \]
   5. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(-1, \color{blue}{a}, b \cdot \left(2 - y\right)\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(-1, a, b \cdot \left(2 - y\right)\right)\right) \]

      3. lower--.f64 70.9

         \[\leadsto \mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(-1, a, b \cdot \left(2 - y\right)\right)\right) \]

   6. Applied rewrites 70.9%

      \[\leadsto \mathsf{fma}\left(1 - y, z, x - \color{blue}{\mathsf{fma}\left(-1, a, b \cdot \left(2 - y\right)\right)}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 88.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -11200:\\ \;\;\;\;\left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, z + \mathsf{fma}\left(t - \left(2 - y\right), b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -11200.0)
   (- (+ x z) (fma a (- t 1.0) (* b (- 2.0 t))))
   (if (<= a 5.5e+38)
     (fma (- z) y (+ z (fma (- t (- 2.0 y)) b x)))
     (- (+ x (* b (- (+ t y) 2.0))) (* a (- t 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -11200.0) {
		tmp = (x + z) - fma(a, (t - 1.0), (b * (2.0 - t)));
	} else if (a <= 5.5e+38) {
		tmp = fma(-z, y, (z + fma((t - (2.0 - y)), b, x)));
	} else {
		tmp = (x + (b * ((t + y) - 2.0))) - (a * (t - 1.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -11200.0)
		tmp = Float64(Float64(x + z) - fma(a, Float64(t - 1.0), Float64(b * Float64(2.0 - t))));
	elseif (a <= 5.5e+38)
		tmp = fma(Float64(-z), y, Float64(z + fma(Float64(t - Float64(2.0 - y)), b, x)));
	else
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(t + y) - 2.0))) - Float64(a * Float64(t - 1.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -11200.0], N[(N[(x + z), $MachinePrecision] - N[(a * N[(t - 1.0), $MachinePrecision] + N[(b * N[(2.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e+38], N[((-z) * y + N[(z + N[(N[(t - N[(2.0 - y), $MachinePrecision]), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -11200

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, \color{blue}{t - 1}, b \cdot \left(2 - t\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - \color{blue}{1}, b \cdot \left(2 - t\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

      6. lower--.f64 70.4

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

   6. Applied rewrites 70.4%

      \[\leadsto \color{blue}{\left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right)} \]

   if -11200 < a < 5.5000000000000003e38

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right) \]

      5. lower-+.f64 N/A

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right) \]

      6. lower-*.f64 N/A

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

      7. lower--.f64 73.7

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

   4. Applied rewrites 73.7%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

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

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \cdot z} \]

      5. lift--.f64 N/A

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \cdot z \]

      6. sub-negate-rev N/A

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(1 - y\right) \cdot z \]

      7. lift--.f64 N/A

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(1 - y\right) \cdot z \]

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

          \[\leadsto z \cdot \left(1 - y\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. sub-flip N/A

          \[\leadsto z \cdot \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. distribute-rgt-in N/A

          \[\leadsto \left(1 \cdot z + \left(\mathsf{neg}\left(y\right)\right) \cdot z\right) + \left(\color{blue}{x} + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

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

          \[\leadsto \left(1 \cdot z + \left(\mathsf{neg}\left(y \cdot z\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \left(1 \cdot z + \left(\mathsf{neg}\left(y \cdot z\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \left(1 \cdot z + -1 \cdot \left(y \cdot z\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \left(1 \cdot z + -1 \cdot \left(y \cdot z\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      17. *-lft-identity N/A

          \[\leadsto \left(z + -1 \cdot \left(y \cdot z\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      18. +-commutative N/A

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

      19. associate-+l+ N/A

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

   6. Applied rewrites 74.8%

      \[\leadsto \mathsf{fma}\left(-z, \color{blue}{y}, z + \mathsf{fma}\left(t - \left(2 - y\right), b, x\right)\right) \]

   if 5.5000000000000003e38 < a

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right) \]

      5. lower-+.f64 N/A

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right) \]

      6. lower-*.f64 N/A

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

      7. lower--.f64 74.1

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

   4. Applied rewrites 74.1%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-z, y, z + \mathsf{fma}\left(t - \left(2 - y\right), b, x\right)\right)\\ \mathbf{if}\;y \leq -0.000195:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+53}:\\ \;\;\;\;\left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- z) y (+ z (fma (- t (- 2.0 y)) b x)))))
   (if (<= y -0.000195)
     t_1
     (if (<= y 2.9e+53) (- (+ x z) (fma a (- t 1.0) (* b (- 2.0 t)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(-z, y, (z + fma((t - (2.0 - y)), b, x)));
	double tmp;
	if (y <= -0.000195) {
		tmp = t_1;
	} else if (y <= 2.9e+53) {
		tmp = (x + z) - fma(a, (t - 1.0), (b * (2.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(-z), y, Float64(z + fma(Float64(t - Float64(2.0 - y)), b, x)))
	tmp = 0.0
	if (y <= -0.000195)
		tmp = t_1;
	elseif (y <= 2.9e+53)
		tmp = Float64(Float64(x + z) - fma(a, Float64(t - 1.0), Float64(b * Float64(2.0 - t))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-z) * y + N[(z + N[(N[(t - N[(2.0 - y), $MachinePrecision]), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.000195], t$95$1, If[LessEqual[y, 2.9e+53], N[(N[(x + z), $MachinePrecision] - N[(a * N[(t - 1.0), $MachinePrecision] + N[(b * N[(2.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.94999999999999996e-4 or 2.9000000000000002e53 < y

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right) \]

      5. lower-+.f64 N/A

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right) \]

      6. lower-*.f64 N/A

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

      7. lower--.f64 73.7

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

   4. Applied rewrites 73.7%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

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

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \cdot z} \]

      5. lift--.f64 N/A

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \cdot z \]

      6. sub-negate-rev N/A

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(1 - y\right) \cdot z \]

      7. lift--.f64 N/A

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(1 - y\right) \cdot z \]

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

          \[\leadsto z \cdot \left(1 - y\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. sub-flip N/A

          \[\leadsto z \cdot \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. distribute-rgt-in N/A

          \[\leadsto \left(1 \cdot z + \left(\mathsf{neg}\left(y\right)\right) \cdot z\right) + \left(\color{blue}{x} + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

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

          \[\leadsto \left(1 \cdot z + \left(\mathsf{neg}\left(y \cdot z\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \left(1 \cdot z + \left(\mathsf{neg}\left(y \cdot z\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \left(1 \cdot z + -1 \cdot \left(y \cdot z\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \left(1 \cdot z + -1 \cdot \left(y \cdot z\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      17. *-lft-identity N/A

          \[\leadsto \left(z + -1 \cdot \left(y \cdot z\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      18. +-commutative N/A

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

      19. associate-+l+ N/A

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

   6. Applied rewrites 74.8%

      \[\leadsto \mathsf{fma}\left(-z, \color{blue}{y}, z + \mathsf{fma}\left(t - \left(2 - y\right), b, x\right)\right) \]

   if -1.94999999999999996e-4 < y < 2.9000000000000002e53

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, \color{blue}{t - 1}, b \cdot \left(2 - t\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - \color{blue}{1}, b \cdot \left(2 - t\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

      6. lower--.f64 70.4

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

   6. Applied rewrites 70.4%

      \[\leadsto \color{blue}{\left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 84.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - \left(2 - y\right), b, \left(-z\right) \cdot y\right)\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+54}:\\ \;\;\;\;\left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- t (- 2.0 y)) b (* (- z) y))))
   (if (<= y -4.6e+69)
     t_1
     (if (<= y 2.4e+54) (- (+ x z) (fma a (- t 1.0) (* b (- 2.0 t)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((t - (2.0 - y)), b, (-z * y));
	double tmp;
	if (y <= -4.6e+69) {
		tmp = t_1;
	} else if (y <= 2.4e+54) {
		tmp = (x + z) - fma(a, (t - 1.0), (b * (2.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(t - Float64(2.0 - y)), b, Float64(Float64(-z) * y))
	tmp = 0.0
	if (y <= -4.6e+69)
		tmp = t_1;
	elseif (y <= 2.4e+54)
		tmp = Float64(Float64(x + z) - fma(a, Float64(t - 1.0), Float64(b * Float64(2.0 - t))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - N[(2.0 - y), $MachinePrecision]), $MachinePrecision] * b + N[((-z) * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.6e+69], t$95$1, If[LessEqual[y, 2.4e+54], N[(N[(x + z), $MachinePrecision] - N[(a * N[(t - 1.0), $MachinePrecision] + N[(b * N[(2.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.60000000000000033e69 or 2.39999999999999998e54 < y

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 50.2

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

   4. Applied rewrites 50.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 51.1

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, -1 \cdot \left(y \cdot z\right)\right)} \]

      5. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + t\right) - 2}, b, -1 \cdot \left(y \cdot z\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, -1 \cdot \left(y \cdot z\right)\right) \]

      7. associate--l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{y + \left(t - 2\right)}, b, -1 \cdot \left(y \cdot z\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t - 2\right) + y}, b, -1 \cdot \left(y \cdot z\right)\right) \]

      9. associate--r- N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{t - \left(2 - y\right)}, b, -1 \cdot \left(y \cdot z\right)\right) \]

      10. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(t - \color{blue}{\left(2 - y\right)}, b, -1 \cdot \left(y \cdot z\right)\right) \]

      11. lower--.f64 51.1

          \[\leadsto \mathsf{fma}\left(\color{blue}{t - \left(2 - y\right)}, b, -1 \cdot \left(y \cdot z\right)\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(t - \left(2 - y\right), b, -1 \cdot \color{blue}{\left(y \cdot z\right)}\right) \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(t - \left(2 - y\right), b, \mathsf{neg}\left(y \cdot z\right)\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(t - \left(2 - y\right), b, \mathsf{neg}\left(y \cdot z\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(t - \left(2 - y\right), b, \mathsf{neg}\left(z \cdot y\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(t - \left(2 - y\right), b, \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{y}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(t - \left(2 - y\right), b, \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{y}\right) \]

      18. lower-neg.f64 51.1

          \[\leadsto \mathsf{fma}\left(t - \left(2 - y\right), b, \left(-z\right) \cdot y\right) \]

   6. Applied rewrites 51.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - \left(2 - y\right), b, \left(-z\right) \cdot y\right)} \]

   if -4.60000000000000033e69 < y < 2.39999999999999998e54

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, \color{blue}{t - 1}, b \cdot \left(2 - t\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - \color{blue}{1}, b \cdot \left(2 - t\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

      6. lower--.f64 70.4

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

   6. Applied rewrites 70.4%

      \[\leadsto \color{blue}{\left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 70.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - \left(2 - y\right)\right) \cdot b\\ \mathbf{if}\;b \leq -6.1 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{-96}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x - -1 \cdot a\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+120}:\\ \;\;\;\;\left(x + z\right) - a \cdot \left(t - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t (- 2.0 y)) b)))
   (if (<= b -6.1e+64)
     t_1
     (if (<= b -3.7e-96)
       (fma (- 1.0 y) z (- x (* -1.0 a)))
       (if (<= b 3.7e+120) (- (+ x z) (* a (- t 1.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - (2.0 - y)) * b;
	double tmp;
	if (b <= -6.1e+64) {
		tmp = t_1;
	} else if (b <= -3.7e-96) {
		tmp = fma((1.0 - y), z, (x - (-1.0 * a)));
	} else if (b <= 3.7e+120) {
		tmp = (x + z) - (a * (t - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - Float64(2.0 - y)) * b)
	tmp = 0.0
	if (b <= -6.1e+64)
		tmp = t_1;
	elseif (b <= -3.7e-96)
		tmp = fma(Float64(1.0 - y), z, Float64(x - Float64(-1.0 * a)));
	elseif (b <= 3.7e+120)
		tmp = Float64(Float64(x + z) - Float64(a * Float64(t - 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - N[(2.0 - y), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -6.1e+64], t$95$1, If[LessEqual[b, -3.7e-96], N[(N[(1.0 - y), $MachinePrecision] * z + N[(x - N[(-1.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e+120], N[(N[(x + z), $MachinePrecision] - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.1000000000000001e64 or 3.70000000000000024e120 < b

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in b around -inf

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

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(2 - \left(t + y\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(2 - \color{blue}{\left(t + y\right)}\right)\right) \]

      4. lower-+.f64 37.8

         \[\leadsto -1 \cdot \left(b \cdot \left(2 - \left(t + \color{blue}{y}\right)\right)\right) \]

   6. Applied rewrites 37.8%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(b \cdot \left(2 - \left(t + y\right)\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(b \cdot \left(2 - \left(t + y\right)\right)\right) \]

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

         \[\leadsto b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(2 - \left(t + y\right)\right)\right)\right)} \]

      5. lift--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(2 - \left(t + y\right)\right)\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(2 - \left(t + y\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(2 - \left(y + t\right)\right)\right)\right) \]

      8. sub-negate-rev N/A

         \[\leadsto b \cdot \left(\left(y + t\right) - \color{blue}{2}\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot \color{blue}{b} \]

      10. lower-*.f64 N/A

          \[\leadsto \left(\left(y + t\right) - 2\right) \cdot \color{blue}{b} \]

      11. sub-negate-rev N/A

          \[\leadsto \left(\mathsf{neg}\left(\left(2 - \left(y + t\right)\right)\right)\right) \cdot b \]

      12. associate--l- N/A

          \[\leadsto \left(\mathsf{neg}\left(\left(\left(2 - y\right) - t\right)\right)\right) \cdot b \]

      13. sub-negate-rev N/A

          \[\leadsto \left(t - \left(2 - y\right)\right) \cdot b \]

      14. lower--.f64 N/A

          \[\leadsto \left(t - \left(2 - y\right)\right) \cdot b \]

      15. lower--.f64 37.8

          \[\leadsto \left(t - \left(2 - y\right)\right) \cdot b \]

   8. Applied rewrites 37.8%

      \[\leadsto \left(t - \left(2 - y\right)\right) \cdot \color{blue}{b} \]

   if -6.1000000000000001e64 < b < -3.69999999999999986e-96

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(1 - y, z, x - \color{blue}{\left(-1 \cdot a + b \cdot \left(2 - y\right)\right)}\right) \]
   5. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(-1, \color{blue}{a}, b \cdot \left(2 - y\right)\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(-1, a, b \cdot \left(2 - y\right)\right)\right) \]

      3. lower--.f64 70.9

         \[\leadsto \mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(-1, a, b \cdot \left(2 - y\right)\right)\right) \]

   6. Applied rewrites 70.9%

      \[\leadsto \mathsf{fma}\left(1 - y, z, x - \color{blue}{\mathsf{fma}\left(-1, a, b \cdot \left(2 - y\right)\right)}\right) \]

   7. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(1 - y, z, x - -1 \cdot \color{blue}{a}\right) \]
   8. Step-by-step derivation

      1. lower-*.f64 50.8

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

   9. Applied rewrites 50.8%

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

   if -3.69999999999999986e-96 < b < 3.70000000000000024e120

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, \color{blue}{t - 1}, b \cdot \left(2 - t\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - \color{blue}{1}, b \cdot \left(2 - t\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

      6. lower--.f64 70.4

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

   6. Applied rewrites 70.4%

      \[\leadsto \color{blue}{\left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right)} \]

   7. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 51.4

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

   9. Applied rewrites 51.4%

      \[\leadsto \left(x + z\right) - a \cdot \color{blue}{\left(t - 1\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 69.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - \left(2 - y\right), b, \left(-z\right) \cdot y\right)\\ \mathbf{if}\;b \leq -1.46 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+120}:\\ \;\;\;\;\left(x + z\right) - a \cdot \left(t - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- t (- 2.0 y)) b (* (- z) y))))
   (if (<= b -1.46e+60)
     t_1
     (if (<= b 3.3e+120) (- (+ x z) (* a (- t 1.0))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((t - (2.0 - y)), b, (-z * y));
	double tmp;
	if (b <= -1.46e+60) {
		tmp = t_1;
	} else if (b <= 3.3e+120) {
		tmp = (x + z) - (a * (t - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(t - Float64(2.0 - y)), b, Float64(Float64(-z) * y))
	tmp = 0.0
	if (b <= -1.46e+60)
		tmp = t_1;
	elseif (b <= 3.3e+120)
		tmp = Float64(Float64(x + z) - Float64(a * Float64(t - 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - N[(2.0 - y), $MachinePrecision]), $MachinePrecision] * b + N[((-z) * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.46e+60], t$95$1, If[LessEqual[b, 3.3e+120], N[(N[(x + z), $MachinePrecision] - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.4600000000000001e60 or 3.29999999999999991e120 < b

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 50.2

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

   4. Applied rewrites 50.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 51.1

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, -1 \cdot \left(y \cdot z\right)\right)} \]

      5. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + t\right) - 2}, b, -1 \cdot \left(y \cdot z\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, -1 \cdot \left(y \cdot z\right)\right) \]

      7. associate--l+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{y + \left(t - 2\right)}, b, -1 \cdot \left(y \cdot z\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t - 2\right) + y}, b, -1 \cdot \left(y \cdot z\right)\right) \]

      9. associate--r- N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{t - \left(2 - y\right)}, b, -1 \cdot \left(y \cdot z\right)\right) \]

      10. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(t - \color{blue}{\left(2 - y\right)}, b, -1 \cdot \left(y \cdot z\right)\right) \]

      11. lower--.f64 51.1

          \[\leadsto \mathsf{fma}\left(\color{blue}{t - \left(2 - y\right)}, b, -1 \cdot \left(y \cdot z\right)\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(t - \left(2 - y\right), b, -1 \cdot \color{blue}{\left(y \cdot z\right)}\right) \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(t - \left(2 - y\right), b, \mathsf{neg}\left(y \cdot z\right)\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(t - \left(2 - y\right), b, \mathsf{neg}\left(y \cdot z\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(t - \left(2 - y\right), b, \mathsf{neg}\left(z \cdot y\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(t - \left(2 - y\right), b, \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{y}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(t - \left(2 - y\right), b, \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{y}\right) \]

      18. lower-neg.f64 51.1

          \[\leadsto \mathsf{fma}\left(t - \left(2 - y\right), b, \left(-z\right) \cdot y\right) \]

   6. Applied rewrites 51.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - \left(2 - y\right), b, \left(-z\right) \cdot y\right)} \]

   if -1.4600000000000001e60 < b < 3.29999999999999991e120

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, \color{blue}{t - 1}, b \cdot \left(2 - t\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - \color{blue}{1}, b \cdot \left(2 - t\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

      6. lower--.f64 70.4

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

   6. Applied rewrites 70.4%

      \[\leadsto \color{blue}{\left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right)} \]

   7. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 51.4

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

   9. Applied rewrites 51.4%

      \[\leadsto \left(x + z\right) - a \cdot \color{blue}{\left(t - 1\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 69.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - \left(2 - y\right)\right) \cdot b\\ \mathbf{if}\;b \leq -2.4 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+120}:\\ \;\;\;\;\left(x + z\right) - a \cdot \left(t - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t (- 2.0 y)) b)))
   (if (<= b -2.4e+65)
     t_1
     (if (<= b 3.7e+120) (- (+ x z) (* a (- t 1.0))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - (2.0 - y)) * b;
	double tmp;
	if (b <= -2.4e+65) {
		tmp = t_1;
	} else if (b <= 3.7e+120) {
		tmp = (x + z) - (a * (t - 1.0));
	} 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 - (2.0d0 - y)) * b
    if (b <= (-2.4d+65)) then
        tmp = t_1
    else if (b <= 3.7d+120) then
        tmp = (x + z) - (a * (t - 1.0d0))
    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 - (2.0 - y)) * b;
	double tmp;
	if (b <= -2.4e+65) {
		tmp = t_1;
	} else if (b <= 3.7e+120) {
		tmp = (x + z) - (a * (t - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - (2.0 - y)) * b
	tmp = 0
	if b <= -2.4e+65:
		tmp = t_1
	elif b <= 3.7e+120:
		tmp = (x + z) - (a * (t - 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - Float64(2.0 - y)) * b)
	tmp = 0.0
	if (b <= -2.4e+65)
		tmp = t_1;
	elseif (b <= 3.7e+120)
		tmp = Float64(Float64(x + z) - Float64(a * Float64(t - 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - (2.0 - y)) * b;
	tmp = 0.0;
	if (b <= -2.4e+65)
		tmp = t_1;
	elseif (b <= 3.7e+120)
		tmp = (x + z) - (a * (t - 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - N[(2.0 - y), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.4e+65], t$95$1, If[LessEqual[b, 3.7e+120], N[(N[(x + z), $MachinePrecision] - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.4000000000000002e65 or 3.70000000000000024e120 < b

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in b around -inf

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

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(2 - \left(t + y\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(2 - \color{blue}{\left(t + y\right)}\right)\right) \]

      4. lower-+.f64 37.8

         \[\leadsto -1 \cdot \left(b \cdot \left(2 - \left(t + \color{blue}{y}\right)\right)\right) \]

   6. Applied rewrites 37.8%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(b \cdot \left(2 - \left(t + y\right)\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(b \cdot \left(2 - \left(t + y\right)\right)\right) \]

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

         \[\leadsto b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(2 - \left(t + y\right)\right)\right)\right)} \]

      5. lift--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(2 - \left(t + y\right)\right)\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(2 - \left(t + y\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(2 - \left(y + t\right)\right)\right)\right) \]

      8. sub-negate-rev N/A

         \[\leadsto b \cdot \left(\left(y + t\right) - \color{blue}{2}\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot \color{blue}{b} \]

      10. lower-*.f64 N/A

          \[\leadsto \left(\left(y + t\right) - 2\right) \cdot \color{blue}{b} \]

      11. sub-negate-rev N/A

          \[\leadsto \left(\mathsf{neg}\left(\left(2 - \left(y + t\right)\right)\right)\right) \cdot b \]

      12. associate--l- N/A

          \[\leadsto \left(\mathsf{neg}\left(\left(\left(2 - y\right) - t\right)\right)\right) \cdot b \]

      13. sub-negate-rev N/A

          \[\leadsto \left(t - \left(2 - y\right)\right) \cdot b \]

      14. lower--.f64 N/A

          \[\leadsto \left(t - \left(2 - y\right)\right) \cdot b \]

      15. lower--.f64 37.8

          \[\leadsto \left(t - \left(2 - y\right)\right) \cdot b \]

   8. Applied rewrites 37.8%

      \[\leadsto \left(t - \left(2 - y\right)\right) \cdot \color{blue}{b} \]

   if -2.4000000000000002e65 < b < 3.70000000000000024e120

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, \color{blue}{t - 1}, b \cdot \left(2 - t\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - \color{blue}{1}, b \cdot \left(2 - t\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

      6. lower--.f64 70.4

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

   6. Applied rewrites 70.4%

      \[\leadsto \color{blue}{\left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right)} \]

   7. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 51.4

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

   9. Applied rewrites 51.4%

      \[\leadsto \left(x + z\right) - a \cdot \color{blue}{\left(t - 1\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 65.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-40}:\\ \;\;\;\;\left(x + z\right) - b \cdot \left(2 - t\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+55}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1.3e+29)
     t_1
     (if (<= y 1.15e-40)
       (- (+ x z) (* b (- 2.0 t)))
       (if (<= y 3.9e+55) (* a (- 1.0 t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.3e+29) {
		tmp = t_1;
	} else if (y <= 1.15e-40) {
		tmp = (x + z) - (b * (2.0 - t));
	} else if (y <= 3.9e+55) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, 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 * (b - z)
    if (y <= (-1.3d+29)) then
        tmp = t_1
    else if (y <= 1.15d-40) then
        tmp = (x + z) - (b * (2.0d0 - t))
    else if (y <= 3.9d+55) then
        tmp = a * (1.0d0 - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.3e+29) {
		tmp = t_1;
	} else if (y <= 1.15e-40) {
		tmp = (x + z) - (b * (2.0 - t));
	} else if (y <= 3.9e+55) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -1.3e+29:
		tmp = t_1
	elif y <= 1.15e-40:
		tmp = (x + z) - (b * (2.0 - t))
	elif y <= 3.9e+55:
		tmp = a * (1.0 - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.3e+29)
		tmp = t_1;
	elseif (y <= 1.15e-40)
		tmp = Float64(Float64(x + z) - Float64(b * Float64(2.0 - t)));
	elseif (y <= 3.9e+55)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.3e+29)
		tmp = t_1;
	elseif (y <= 1.15e-40)
		tmp = (x + z) - (b * (2.0 - t));
	elseif (y <= 3.9e+55)
		tmp = a * (1.0 - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e+29], t$95$1, If[LessEqual[y, 1.15e-40], N[(N[(x + z), $MachinePrecision] - N[(b * N[(2.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e+55], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3e29 or 3.90000000000000027e55 < y

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 33.0

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

   4. Applied rewrites 33.0%

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

   if -1.3e29 < y < 1.15e-40

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, \color{blue}{t - 1}, b \cdot \left(2 - t\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - \color{blue}{1}, b \cdot \left(2 - t\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

      6. lower--.f64 70.4

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

   6. Applied rewrites 70.4%

      \[\leadsto \color{blue}{\left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right)} \]

   7. Taylor expanded in a around 0

      \[\leadsto \left(x + z\right) - \color{blue}{b \cdot \left(2 - t\right)} \]
   8. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(x + z\right) - b \cdot \color{blue}{\left(2 - t\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x + z\right) - b \cdot \left(\color{blue}{2} - t\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \left(x + z\right) - b \cdot \left(2 - \color{blue}{t}\right) \]

      4. lower--.f64 46.5

         \[\leadsto \left(x + z\right) - b \cdot \left(2 - t\right) \]

   9. Applied rewrites 46.5%

      \[\leadsto \left(x + z\right) - \color{blue}{b \cdot \left(2 - t\right)} \]

   if 1.15e-40 < y < 3.90000000000000027e55

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 28.2

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

   4. Applied rewrites 28.2%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 57.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(2 - t\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -76:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-189}:\\ \;\;\;\;z - t\_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-41}:\\ \;\;\;\;x - t\_1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+55}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- 2.0 t))) (t_2 (* y (- b z))))
   (if (<= y -76.0)
     t_2
     (if (<= y -1.55e-189)
       (- z t_1)
       (if (<= y 2e-41) (- x t_1) (if (<= y 3.9e+55) (* a (- 1.0 t)) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (2.0 - t);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -76.0) {
		tmp = t_2;
	} else if (y <= -1.55e-189) {
		tmp = z - t_1;
	} else if (y <= 2e-41) {
		tmp = x - t_1;
	} else if (y <= 3.9e+55) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, 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) :: t_2
    real(8) :: tmp
    t_1 = b * (2.0d0 - t)
    t_2 = y * (b - z)
    if (y <= (-76.0d0)) then
        tmp = t_2
    else if (y <= (-1.55d-189)) then
        tmp = z - t_1
    else if (y <= 2d-41) then
        tmp = x - t_1
    else if (y <= 3.9d+55) then
        tmp = a * (1.0d0 - t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (2.0 - t);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -76.0) {
		tmp = t_2;
	} else if (y <= -1.55e-189) {
		tmp = z - t_1;
	} else if (y <= 2e-41) {
		tmp = x - t_1;
	} else if (y <= 3.9e+55) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (2.0 - t)
	t_2 = y * (b - z)
	tmp = 0
	if y <= -76.0:
		tmp = t_2
	elif y <= -1.55e-189:
		tmp = z - t_1
	elif y <= 2e-41:
		tmp = x - t_1
	elif y <= 3.9e+55:
		tmp = a * (1.0 - t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(2.0 - t))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -76.0)
		tmp = t_2;
	elseif (y <= -1.55e-189)
		tmp = Float64(z - t_1);
	elseif (y <= 2e-41)
		tmp = Float64(x - t_1);
	elseif (y <= 3.9e+55)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (2.0 - t);
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -76.0)
		tmp = t_2;
	elseif (y <= -1.55e-189)
		tmp = z - t_1;
	elseif (y <= 2e-41)
		tmp = x - t_1;
	elseif (y <= 3.9e+55)
		tmp = a * (1.0 - t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(2.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -76.0], t$95$2, If[LessEqual[y, -1.55e-189], N[(z - t$95$1), $MachinePrecision], If[LessEqual[y, 2e-41], N[(x - t$95$1), $MachinePrecision], If[LessEqual[y, 3.9e+55], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -76 or 3.90000000000000027e55 < y

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 33.0

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

   4. Applied rewrites 33.0%

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

   if -76 < y < -1.55e-189

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, \color{blue}{t - 1}, b \cdot \left(2 - t\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - \color{blue}{1}, b \cdot \left(2 - t\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

      6. lower--.f64 70.4

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

   6. Applied rewrites 70.4%

      \[\leadsto \color{blue}{\left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right)} \]

   7. Taylor expanded in a around 0

      \[\leadsto \left(x + z\right) - \color{blue}{b \cdot \left(2 - t\right)} \]
   8. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(x + z\right) - b \cdot \color{blue}{\left(2 - t\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x + z\right) - b \cdot \left(\color{blue}{2} - t\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \left(x + z\right) - b \cdot \left(2 - \color{blue}{t}\right) \]

      4. lower--.f64 46.5

         \[\leadsto \left(x + z\right) - b \cdot \left(2 - t\right) \]

   9. Applied rewrites 46.5%

      \[\leadsto \left(x + z\right) - \color{blue}{b \cdot \left(2 - t\right)} \]

   10. Taylor expanded in x around 0

       \[\leadsto z - b \cdot \left(\color{blue}{2} - t\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 32.6%

       \[\leadsto z - b \cdot \left(\color{blue}{2} - t\right) \]

   if -1.55e-189 < y < 2.00000000000000001e-41

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, \color{blue}{t - 1}, b \cdot \left(2 - t\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - \color{blue}{1}, b \cdot \left(2 - t\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

      6. lower--.f64 70.4

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

   6. Applied rewrites 70.4%

      \[\leadsto \color{blue}{\left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right)} \]

   7. Taylor expanded in a around 0

      \[\leadsto \left(x + z\right) - \color{blue}{b \cdot \left(2 - t\right)} \]
   8. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(x + z\right) - b \cdot \color{blue}{\left(2 - t\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x + z\right) - b \cdot \left(\color{blue}{2} - t\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \left(x + z\right) - b \cdot \left(2 - \color{blue}{t}\right) \]

      4. lower--.f64 46.5

         \[\leadsto \left(x + z\right) - b \cdot \left(2 - t\right) \]

   9. Applied rewrites 46.5%

      \[\leadsto \left(x + z\right) - \color{blue}{b \cdot \left(2 - t\right)} \]

   10. Taylor expanded in z around 0

       \[\leadsto x - b \cdot \color{blue}{\left(2 - t\right)} \]
   11. Step-by-step derivation

       1. lower--.f64 N/A

          \[\leadsto x - b \cdot \left(2 - \color{blue}{t}\right) \]

       2. lower-*.f64 N/A

          \[\leadsto x - b \cdot \left(2 - t\right) \]

       3. lower--.f64 37.3

          \[\leadsto x - b \cdot \left(2 - t\right) \]

   12. Applied rewrites 37.3%

       \[\leadsto x - b \cdot \color{blue}{\left(2 - t\right)} \]

   if 2.00000000000000001e-41 < y < 3.90000000000000027e55

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 28.2

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

   4. Applied rewrites 28.2%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 11: 56.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-41}:\\ \;\;\;\;x - b \cdot \left(2 - t\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+55}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1.3e+29)
     t_1
     (if (<= y 2e-41)
       (- x (* b (- 2.0 t)))
       (if (<= y 3.9e+55) (* a (- 1.0 t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.3e+29) {
		tmp = t_1;
	} else if (y <= 2e-41) {
		tmp = x - (b * (2.0 - t));
	} else if (y <= 3.9e+55) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, 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 * (b - z)
    if (y <= (-1.3d+29)) then
        tmp = t_1
    else if (y <= 2d-41) then
        tmp = x - (b * (2.0d0 - t))
    else if (y <= 3.9d+55) then
        tmp = a * (1.0d0 - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.3e+29) {
		tmp = t_1;
	} else if (y <= 2e-41) {
		tmp = x - (b * (2.0 - t));
	} else if (y <= 3.9e+55) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -1.3e+29:
		tmp = t_1
	elif y <= 2e-41:
		tmp = x - (b * (2.0 - t))
	elif y <= 3.9e+55:
		tmp = a * (1.0 - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.3e+29)
		tmp = t_1;
	elseif (y <= 2e-41)
		tmp = Float64(x - Float64(b * Float64(2.0 - t)));
	elseif (y <= 3.9e+55)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.3e+29)
		tmp = t_1;
	elseif (y <= 2e-41)
		tmp = x - (b * (2.0 - t));
	elseif (y <= 3.9e+55)
		tmp = a * (1.0 - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e+29], t$95$1, If[LessEqual[y, 2e-41], N[(x - N[(b * N[(2.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e+55], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3e29 or 3.90000000000000027e55 < y

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 33.0

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

   4. Applied rewrites 33.0%

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

   if -1.3e29 < y < 2.00000000000000001e-41

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, \color{blue}{t - 1}, b \cdot \left(2 - t\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - \color{blue}{1}, b \cdot \left(2 - t\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

      6. lower--.f64 70.4

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

   6. Applied rewrites 70.4%

      \[\leadsto \color{blue}{\left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right)} \]

   7. Taylor expanded in a around 0

      \[\leadsto \left(x + z\right) - \color{blue}{b \cdot \left(2 - t\right)} \]
   8. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(x + z\right) - b \cdot \color{blue}{\left(2 - t\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x + z\right) - b \cdot \left(\color{blue}{2} - t\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \left(x + z\right) - b \cdot \left(2 - \color{blue}{t}\right) \]

      4. lower--.f64 46.5

         \[\leadsto \left(x + z\right) - b \cdot \left(2 - t\right) \]

   9. Applied rewrites 46.5%

      \[\leadsto \left(x + z\right) - \color{blue}{b \cdot \left(2 - t\right)} \]

   10. Taylor expanded in z around 0

       \[\leadsto x - b \cdot \color{blue}{\left(2 - t\right)} \]
   11. Step-by-step derivation

       1. lower--.f64 N/A

          \[\leadsto x - b \cdot \left(2 - \color{blue}{t}\right) \]

       2. lower-*.f64 N/A

          \[\leadsto x - b \cdot \left(2 - t\right) \]

       3. lower--.f64 37.3

          \[\leadsto x - b \cdot \left(2 - t\right) \]

   12. Applied rewrites 37.3%

       \[\leadsto x - b \cdot \color{blue}{\left(2 - t\right)} \]

   if 2.00000000000000001e-41 < y < 3.90000000000000027e55

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 28.2

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

   4. Applied rewrites 28.2%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 56.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+28}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, b \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -4.6e+50)
     t_1
     (if (<= t 1.05e+28) (fma (- 1.0 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 * (b - a);
	double tmp;
	if (t <= -4.6e+50) {
		tmp = t_1;
	} else if (t <= 1.05e+28) {
		tmp = fma((1.0 - y), z, (b * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -4.6e+50)
		tmp = t_1;
	elseif (t <= 1.05e+28)
		tmp = fma(Float64(1.0 - y), z, Float64(b * y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.6e+50], t$95$1, If[LessEqual[t, 1.05e+28], N[(N[(1.0 - y), $MachinePrecision] * z + N[(b * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.59999999999999994e50 or 1.04999999999999995e28 < t

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 32.7

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

   4. Applied rewrites 32.7%

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

   if -4.59999999999999994e50 < t < 1.04999999999999995e28

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{b \cdot y}\right) \]
   5. Step-by-step derivation

      1. lower-*.f64 41.3

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

   6. Applied rewrites 41.3%

      \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{b \cdot y}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 51.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-203}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-105}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+24}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -4.8e+45)
     t_1
     (if (<= t 2.5e-203)
       (* y (- b z))
       (if (<= t 9.2e-105)
         (* (- y 2.0) b)
         (if (<= t 6e+24) (* z (- 1.0 y)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -4.8e+45) {
		tmp = t_1;
	} else if (t <= 2.5e-203) {
		tmp = y * (b - z);
	} else if (t <= 9.2e-105) {
		tmp = (y - 2.0) * b;
	} else if (t <= 6e+24) {
		tmp = z * (1.0 - 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 * (b - a)
    if (t <= (-4.8d+45)) then
        tmp = t_1
    else if (t <= 2.5d-203) then
        tmp = y * (b - z)
    else if (t <= 9.2d-105) then
        tmp = (y - 2.0d0) * b
    else if (t <= 6d+24) then
        tmp = z * (1.0d0 - 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 * (b - a);
	double tmp;
	if (t <= -4.8e+45) {
		tmp = t_1;
	} else if (t <= 2.5e-203) {
		tmp = y * (b - z);
	} else if (t <= 9.2e-105) {
		tmp = (y - 2.0) * b;
	} else if (t <= 6e+24) {
		tmp = z * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -4.8e+45:
		tmp = t_1
	elif t <= 2.5e-203:
		tmp = y * (b - z)
	elif t <= 9.2e-105:
		tmp = (y - 2.0) * b
	elif t <= 6e+24:
		tmp = z * (1.0 - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -4.8e+45)
		tmp = t_1;
	elseif (t <= 2.5e-203)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 9.2e-105)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (t <= 6e+24)
		tmp = Float64(z * Float64(1.0 - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -4.8e+45)
		tmp = t_1;
	elseif (t <= 2.5e-203)
		tmp = y * (b - z);
	elseif (t <= 9.2e-105)
		tmp = (y - 2.0) * b;
	elseif (t <= 6e+24)
		tmp = z * (1.0 - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.8e+45], t$95$1, If[LessEqual[t, 2.5e-203], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e-105], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, 6e+24], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.79999999999999979e45 or 5.9999999999999999e24 < t

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 32.7

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

   4. Applied rewrites 32.7%

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

   if -4.79999999999999979e45 < t < 2.5000000000000001e-203

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 33.0

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

   4. Applied rewrites 33.0%

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

   if 2.5000000000000001e-203 < t < 9.2000000000000004e-105

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in b around -inf

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

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(2 - \left(t + y\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(2 - \color{blue}{\left(t + y\right)}\right)\right) \]

      4. lower-+.f64 37.8

         \[\leadsto -1 \cdot \left(b \cdot \left(2 - \left(t + \color{blue}{y}\right)\right)\right) \]

   6. Applied rewrites 37.8%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(b \cdot \left(2 - \left(t + y\right)\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(b \cdot \left(2 - \left(t + y\right)\right)\right) \]

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

         \[\leadsto b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(2 - \left(t + y\right)\right)\right)\right)} \]

      5. lift--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(2 - \left(t + y\right)\right)\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(2 - \left(t + y\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(2 - \left(y + t\right)\right)\right)\right) \]

      8. sub-negate-rev N/A

         \[\leadsto b \cdot \left(\left(y + t\right) - \color{blue}{2}\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot \color{blue}{b} \]

      10. lower-*.f64 N/A

          \[\leadsto \left(\left(y + t\right) - 2\right) \cdot \color{blue}{b} \]

      11. sub-negate-rev N/A

          \[\leadsto \left(\mathsf{neg}\left(\left(2 - \left(y + t\right)\right)\right)\right) \cdot b \]

      12. associate--l- N/A

          \[\leadsto \left(\mathsf{neg}\left(\left(\left(2 - y\right) - t\right)\right)\right) \cdot b \]

      13. sub-negate-rev N/A

          \[\leadsto \left(t - \left(2 - y\right)\right) \cdot b \]

      14. lower--.f64 N/A

          \[\leadsto \left(t - \left(2 - y\right)\right) \cdot b \]

      15. lower--.f64 37.8

          \[\leadsto \left(t - \left(2 - y\right)\right) \cdot b \]

   8. Applied rewrites 37.8%

      \[\leadsto \left(t - \left(2 - y\right)\right) \cdot \color{blue}{b} \]

   9. Taylor expanded in t around 0

      \[\leadsto \left(y - 2\right) \cdot b \]
   10. Step-by-step derivation

       1. lower--.f64 24.6

          \[\leadsto \left(y - 2\right) \cdot b \]

   11. Applied rewrites 24.6%

       \[\leadsto \left(y - 2\right) \cdot b \]

   if 9.2000000000000004e-105 < t < 5.9999999999999999e24

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 27.8

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

   4. Applied rewrites 27.8%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 14: 50.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+24}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -4.8e+45) t_1 (if (<= t 8.5e+24) (* y (- b z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -4.8e+45) {
		tmp = t_1;
	} else if (t <= 8.5e+24) {
		tmp = y * (b - 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 * (b - a)
    if (t <= (-4.8d+45)) then
        tmp = t_1
    else if (t <= 8.5d+24) then
        tmp = y * (b - 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 * (b - a);
	double tmp;
	if (t <= -4.8e+45) {
		tmp = t_1;
	} else if (t <= 8.5e+24) {
		tmp = y * (b - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -4.8e+45:
		tmp = t_1
	elif t <= 8.5e+24:
		tmp = y * (b - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -4.8e+45)
		tmp = t_1;
	elseif (t <= 8.5e+24)
		tmp = Float64(y * Float64(b - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -4.8e+45)
		tmp = t_1;
	elseif (t <= 8.5e+24)
		tmp = y * (b - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.8e+45], t$95$1, If[LessEqual[t, 8.5e+24], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.79999999999999979e45 or 8.49999999999999959e24 < t

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 32.7

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

   4. Applied rewrites 32.7%

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

   if -4.79999999999999979e45 < t < 8.49999999999999959e24

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 33.0

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

   4. Applied rewrites 33.0%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 48.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 0.7:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -4.8e+45) t_1 (if (<= t 0.7) (* (- y 2.0) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -4.8e+45) {
		tmp = t_1;
	} else if (t <= 0.7) {
		tmp = (y - 2.0) * 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 * (b - a)
    if (t <= (-4.8d+45)) then
        tmp = t_1
    else if (t <= 0.7d0) then
        tmp = (y - 2.0d0) * 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 * (b - a);
	double tmp;
	if (t <= -4.8e+45) {
		tmp = t_1;
	} else if (t <= 0.7) {
		tmp = (y - 2.0) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -4.8e+45:
		tmp = t_1
	elif t <= 0.7:
		tmp = (y - 2.0) * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -4.8e+45)
		tmp = t_1;
	elseif (t <= 0.7)
		tmp = Float64(Float64(y - 2.0) * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -4.8e+45)
		tmp = t_1;
	elseif (t <= 0.7)
		tmp = (y - 2.0) * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.8e+45], t$95$1, If[LessEqual[t, 0.7], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.79999999999999979e45 or 0.69999999999999996 < t

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 32.7

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

   4. Applied rewrites 32.7%

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

   if -4.79999999999999979e45 < t < 0.69999999999999996

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in b around -inf

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

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(2 - \left(t + y\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(2 - \color{blue}{\left(t + y\right)}\right)\right) \]

      4. lower-+.f64 37.8

         \[\leadsto -1 \cdot \left(b \cdot \left(2 - \left(t + \color{blue}{y}\right)\right)\right) \]

   6. Applied rewrites 37.8%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(b \cdot \left(2 - \left(t + y\right)\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(b \cdot \left(2 - \left(t + y\right)\right)\right) \]

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

         \[\leadsto b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(2 - \left(t + y\right)\right)\right)\right)} \]

      5. lift--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(2 - \left(t + y\right)\right)\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(2 - \left(t + y\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(2 - \left(y + t\right)\right)\right)\right) \]

      8. sub-negate-rev N/A

         \[\leadsto b \cdot \left(\left(y + t\right) - \color{blue}{2}\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot \color{blue}{b} \]

      10. lower-*.f64 N/A

          \[\leadsto \left(\left(y + t\right) - 2\right) \cdot \color{blue}{b} \]

      11. sub-negate-rev N/A

          \[\leadsto \left(\mathsf{neg}\left(\left(2 - \left(y + t\right)\right)\right)\right) \cdot b \]

      12. associate--l- N/A

          \[\leadsto \left(\mathsf{neg}\left(\left(\left(2 - y\right) - t\right)\right)\right) \cdot b \]

      13. sub-negate-rev N/A

          \[\leadsto \left(t - \left(2 - y\right)\right) \cdot b \]

      14. lower--.f64 N/A

          \[\leadsto \left(t - \left(2 - y\right)\right) \cdot b \]

      15. lower--.f64 37.8

          \[\leadsto \left(t - \left(2 - y\right)\right) \cdot b \]

   8. Applied rewrites 37.8%

      \[\leadsto \left(t - \left(2 - y\right)\right) \cdot \color{blue}{b} \]

   9. Taylor expanded in t around 0

      \[\leadsto \left(y - 2\right) \cdot b \]
   10. Step-by-step derivation

       1. lower--.f64 24.6

          \[\leadsto \left(y - 2\right) \cdot b \]

   11. Applied rewrites 24.6%

       \[\leadsto \left(y - 2\right) \cdot b \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 39.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -8000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+26}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -8000.0) t_1 (if (<= a 2.4e+26) (* (- y 2.0) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -8000.0) {
		tmp = t_1;
	} else if (a <= 2.4e+26) {
		tmp = (y - 2.0) * 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 = a * (1.0d0 - t)
    if (a <= (-8000.0d0)) then
        tmp = t_1
    else if (a <= 2.4d+26) then
        tmp = (y - 2.0d0) * 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 = a * (1.0 - t);
	double tmp;
	if (a <= -8000.0) {
		tmp = t_1;
	} else if (a <= 2.4e+26) {
		tmp = (y - 2.0) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -8000.0:
		tmp = t_1
	elif a <= 2.4e+26:
		tmp = (y - 2.0) * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -8000.0)
		tmp = t_1;
	elseif (a <= 2.4e+26)
		tmp = Float64(Float64(y - 2.0) * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -8000.0)
		tmp = t_1;
	elseif (a <= 2.4e+26)
		tmp = (y - 2.0) * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8000.0], t$95$1, If[LessEqual[a, 2.4e+26], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -8e3 or 2.40000000000000005e26 < a

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 28.2

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

   4. Applied rewrites 28.2%

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

   if -8e3 < a < 2.40000000000000005e26

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in b around -inf

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

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(2 - \left(t + y\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(2 - \color{blue}{\left(t + y\right)}\right)\right) \]

      4. lower-+.f64 37.8

         \[\leadsto -1 \cdot \left(b \cdot \left(2 - \left(t + \color{blue}{y}\right)\right)\right) \]

   6. Applied rewrites 37.8%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(b \cdot \left(2 - \left(t + y\right)\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(b \cdot \left(2 - \left(t + y\right)\right)\right) \]

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

         \[\leadsto b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(2 - \left(t + y\right)\right)\right)\right)} \]

      5. lift--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(2 - \left(t + y\right)\right)\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(2 - \left(t + y\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(2 - \left(y + t\right)\right)\right)\right) \]

      8. sub-negate-rev N/A

         \[\leadsto b \cdot \left(\left(y + t\right) - \color{blue}{2}\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot \color{blue}{b} \]

      10. lower-*.f64 N/A

          \[\leadsto \left(\left(y + t\right) - 2\right) \cdot \color{blue}{b} \]

      11. sub-negate-rev N/A

          \[\leadsto \left(\mathsf{neg}\left(\left(2 - \left(y + t\right)\right)\right)\right) \cdot b \]

      12. associate--l- N/A

          \[\leadsto \left(\mathsf{neg}\left(\left(\left(2 - y\right) - t\right)\right)\right) \cdot b \]

      13. sub-negate-rev N/A

          \[\leadsto \left(t - \left(2 - y\right)\right) \cdot b \]

      14. lower--.f64 N/A

          \[\leadsto \left(t - \left(2 - y\right)\right) \cdot b \]

      15. lower--.f64 37.8

          \[\leadsto \left(t - \left(2 - y\right)\right) \cdot b \]

   8. Applied rewrites 37.8%

      \[\leadsto \left(t - \left(2 - y\right)\right) \cdot \color{blue}{b} \]

   9. Taylor expanded in t around 0

      \[\leadsto \left(y - 2\right) \cdot b \]
   10. Step-by-step derivation

       1. lower--.f64 24.6

          \[\leadsto \left(y - 2\right) \cdot b \]

   11. Applied rewrites 24.6%

       \[\leadsto \left(y - 2\right) \cdot b \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 33.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+45}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-9}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -9.5e+45)
   (* b t)
   (if (<= t 3.1e-9) (* (- y 2.0) b) (* b (- t 2.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.5e+45) {
		tmp = b * t;
	} else if (t <= 3.1e-9) {
		tmp = (y - 2.0) * b;
	} else {
		tmp = b * (t - 2.0);
	}
	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 (t <= (-9.5d+45)) then
        tmp = b * t
    else if (t <= 3.1d-9) then
        tmp = (y - 2.0d0) * b
    else
        tmp = b * (t - 2.0d0)
    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 (t <= -9.5e+45) {
		tmp = b * t;
	} else if (t <= 3.1e-9) {
		tmp = (y - 2.0) * b;
	} else {
		tmp = b * (t - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9.5e+45:
		tmp = b * t
	elif t <= 3.1e-9:
		tmp = (y - 2.0) * b
	else:
		tmp = b * (t - 2.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9.5e+45)
		tmp = Float64(b * t);
	elseif (t <= 3.1e-9)
		tmp = Float64(Float64(y - 2.0) * b);
	else
		tmp = Float64(b * Float64(t - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -9.5e+45)
		tmp = b * t;
	elseif (t <= 3.1e-9)
		tmp = (y - 2.0) * b;
	else
		tmp = b * (t - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9.5e+45], N[(b * t), $MachinePrecision], If[LessEqual[t, 3.1e-9], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.4999999999999998e45

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in b around -inf

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

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(2 - \left(t + y\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(2 - \color{blue}{\left(t + y\right)}\right)\right) \]

      4. lower-+.f64 37.8

         \[\leadsto -1 \cdot \left(b \cdot \left(2 - \left(t + \color{blue}{y}\right)\right)\right) \]

   6. Applied rewrites 37.8%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]

   7. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{t} \]
   8. Step-by-step derivation

      1. lower-*.f64 17.3

         \[\leadsto b \cdot t \]

   9. Applied rewrites 17.3%

      \[\leadsto b \cdot \color{blue}{t} \]

   if -9.4999999999999998e45 < t < 3.10000000000000005e-9

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in b around -inf

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

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(2 - \left(t + y\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(2 - \color{blue}{\left(t + y\right)}\right)\right) \]

      4. lower-+.f64 37.8

         \[\leadsto -1 \cdot \left(b \cdot \left(2 - \left(t + \color{blue}{y}\right)\right)\right) \]

   6. Applied rewrites 37.8%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(b \cdot \left(2 - \left(t + y\right)\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(b \cdot \left(2 - \left(t + y\right)\right)\right) \]

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

         \[\leadsto b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(2 - \left(t + y\right)\right)\right)\right)} \]

      5. lift--.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(2 - \left(t + y\right)\right)\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(2 - \left(t + y\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(2 - \left(y + t\right)\right)\right)\right) \]

      8. sub-negate-rev N/A

         \[\leadsto b \cdot \left(\left(y + t\right) - \color{blue}{2}\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot \color{blue}{b} \]

      10. lower-*.f64 N/A

          \[\leadsto \left(\left(y + t\right) - 2\right) \cdot \color{blue}{b} \]

      11. sub-negate-rev N/A

          \[\leadsto \left(\mathsf{neg}\left(\left(2 - \left(y + t\right)\right)\right)\right) \cdot b \]

      12. associate--l- N/A

          \[\leadsto \left(\mathsf{neg}\left(\left(\left(2 - y\right) - t\right)\right)\right) \cdot b \]

      13. sub-negate-rev N/A

          \[\leadsto \left(t - \left(2 - y\right)\right) \cdot b \]

      14. lower--.f64 N/A

          \[\leadsto \left(t - \left(2 - y\right)\right) \cdot b \]

      15. lower--.f64 37.8

          \[\leadsto \left(t - \left(2 - y\right)\right) \cdot b \]

   8. Applied rewrites 37.8%

      \[\leadsto \left(t - \left(2 - y\right)\right) \cdot \color{blue}{b} \]

   9. Taylor expanded in t around 0

      \[\leadsto \left(y - 2\right) \cdot b \]
   10. Step-by-step derivation

       1. lower--.f64 24.6

          \[\leadsto \left(y - 2\right) \cdot b \]

   11. Applied rewrites 24.6%

       \[\leadsto \left(y - 2\right) \cdot b \]

   if 3.10000000000000005e-9 < t

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, \color{blue}{t - 1}, b \cdot \left(2 - t\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - \color{blue}{1}, b \cdot \left(2 - t\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

      6. lower--.f64 70.4

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

   6. Applied rewrites 70.4%

      \[\leadsto \color{blue}{\left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right)} \]

   7. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(t - 2\right)} \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(t - \color{blue}{2}\right) \]

      2. lower--.f64 23.4

         \[\leadsto b \cdot \left(t - 2\right) \]

   9. Applied rewrites 23.4%

      \[\leadsto b \cdot \color{blue}{\left(t - 2\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 33.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+47}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 0.0048:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.8e+47) (* y b) (if (<= y 0.0048) (* b (- t 2.0)) (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.8e+47) {
		tmp = y * b;
	} else if (y <= 0.0048) {
		tmp = b * (t - 2.0);
	} else {
		tmp = y * 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 (y <= (-1.8d+47)) then
        tmp = y * b
    else if (y <= 0.0048d0) then
        tmp = b * (t - 2.0d0)
    else
        tmp = y * 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 (y <= -1.8e+47) {
		tmp = y * b;
	} else if (y <= 0.0048) {
		tmp = b * (t - 2.0);
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.8e+47:
		tmp = y * b
	elif y <= 0.0048:
		tmp = b * (t - 2.0)
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.8e+47)
		tmp = Float64(y * b);
	elseif (y <= 0.0048)
		tmp = Float64(b * Float64(t - 2.0));
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.8e+47)
		tmp = y * b;
	elseif (y <= 0.0048)
		tmp = b * (t - 2.0);
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.8e+47], N[(y * b), $MachinePrecision], If[LessEqual[y, 0.0048], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], N[(y * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.80000000000000004e47 or 0.00479999999999999958 < y

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 33.0

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

   4. Applied rewrites 33.0%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 18.5%

      \[\leadsto y \cdot b \]

   if -1.80000000000000004e47 < y < 0.00479999999999999958

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, \color{blue}{t - 1}, b \cdot \left(2 - t\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - \color{blue}{1}, b \cdot \left(2 - t\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

      6. lower--.f64 70.4

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

   6. Applied rewrites 70.4%

      \[\leadsto \color{blue}{\left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right)} \]

   7. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(t - 2\right)} \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(t - \color{blue}{2}\right) \]

      2. lower--.f64 23.4

         \[\leadsto b \cdot \left(t - 2\right) \]

   9. Applied rewrites 23.4%

      \[\leadsto b \cdot \color{blue}{\left(t - 2\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 26.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+45}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-153}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+16}:\\ \;\;\;\;b \cdot -2\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -9.5e+45)
   (* b t)
   (if (<= t 4.6e-153) (* y b) (if (<= t 9e+16) (* b -2.0) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.5e+45) {
		tmp = b * t;
	} else if (t <= 4.6e-153) {
		tmp = y * b;
	} else if (t <= 9e+16) {
		tmp = b * -2.0;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, 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 (t <= (-9.5d+45)) then
        tmp = b * t
    else if (t <= 4.6d-153) then
        tmp = y * b
    else if (t <= 9d+16) then
        tmp = b * (-2.0d0)
    else
        tmp = b * t
    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 (t <= -9.5e+45) {
		tmp = b * t;
	} else if (t <= 4.6e-153) {
		tmp = y * b;
	} else if (t <= 9e+16) {
		tmp = b * -2.0;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9.5e+45:
		tmp = b * t
	elif t <= 4.6e-153:
		tmp = y * b
	elif t <= 9e+16:
		tmp = b * -2.0
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9.5e+45)
		tmp = Float64(b * t);
	elseif (t <= 4.6e-153)
		tmp = Float64(y * b);
	elseif (t <= 9e+16)
		tmp = Float64(b * -2.0);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -9.5e+45)
		tmp = b * t;
	elseif (t <= 4.6e-153)
		tmp = y * b;
	elseif (t <= 9e+16)
		tmp = b * -2.0;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9.5e+45], N[(b * t), $MachinePrecision], If[LessEqual[t, 4.6e-153], N[(y * b), $MachinePrecision], If[LessEqual[t, 9e+16], N[(b * -2.0), $MachinePrecision], N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.4999999999999998e45 or 9e16 < t

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in b around -inf

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

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(2 - \left(t + y\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(2 - \color{blue}{\left(t + y\right)}\right)\right) \]

      4. lower-+.f64 37.8

         \[\leadsto -1 \cdot \left(b \cdot \left(2 - \left(t + \color{blue}{y}\right)\right)\right) \]

   6. Applied rewrites 37.8%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]

   7. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{t} \]
   8. Step-by-step derivation

      1. lower-*.f64 17.3

         \[\leadsto b \cdot t \]

   9. Applied rewrites 17.3%

      \[\leadsto b \cdot \color{blue}{t} \]

   if -9.4999999999999998e45 < t < 4.59999999999999994e-153

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 33.0

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

   4. Applied rewrites 33.0%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 18.5%

      \[\leadsto y \cdot b \]

   if 4.59999999999999994e-153 < t < 9e16

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, \color{blue}{t - 1}, b \cdot \left(2 - t\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - \color{blue}{1}, b \cdot \left(2 - t\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

      6. lower--.f64 70.4

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

   6. Applied rewrites 70.4%

      \[\leadsto \color{blue}{\left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right)} \]

   7. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(t - 2\right)} \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(t - \color{blue}{2}\right) \]

      2. lower--.f64 23.4

         \[\leadsto b \cdot \left(t - 2\right) \]

   9. Applied rewrites 23.4%

      \[\leadsto b \cdot \color{blue}{\left(t - 2\right)} \]

   10. Taylor expanded in t around 0

       \[\leadsto b \cdot -2 \]
   11. Step-by-step derivation

   12. Applied rewrites 8.3%

       \[\leadsto b \cdot -2 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 20: 25.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+28}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-150}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+16}:\\ \;\;\;\;b \cdot -2\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.6e+28)
   (* b t)
   (if (<= t 5.2e-150) a (if (<= t 9e+16) (* b -2.0) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.6e+28) {
		tmp = b * t;
	} else if (t <= 5.2e-150) {
		tmp = a;
	} else if (t <= 9e+16) {
		tmp = b * -2.0;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, 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 (t <= (-3.6d+28)) then
        tmp = b * t
    else if (t <= 5.2d-150) then
        tmp = a
    else if (t <= 9d+16) then
        tmp = b * (-2.0d0)
    else
        tmp = b * t
    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 (t <= -3.6e+28) {
		tmp = b * t;
	} else if (t <= 5.2e-150) {
		tmp = a;
	} else if (t <= 9e+16) {
		tmp = b * -2.0;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.6e+28:
		tmp = b * t
	elif t <= 5.2e-150:
		tmp = a
	elif t <= 9e+16:
		tmp = b * -2.0
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.6e+28)
		tmp = Float64(b * t);
	elseif (t <= 5.2e-150)
		tmp = a;
	elseif (t <= 9e+16)
		tmp = Float64(b * -2.0);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.6e+28)
		tmp = b * t;
	elseif (t <= 5.2e-150)
		tmp = a;
	elseif (t <= 9e+16)
		tmp = b * -2.0;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.6e+28], N[(b * t), $MachinePrecision], If[LessEqual[t, 5.2e-150], a, If[LessEqual[t, 9e+16], N[(b * -2.0), $MachinePrecision], N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.5999999999999999e28 or 9e16 < t

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in b around -inf

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

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(2 - \left(t + y\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(2 - \color{blue}{\left(t + y\right)}\right)\right) \]

      4. lower-+.f64 37.8

         \[\leadsto -1 \cdot \left(b \cdot \left(2 - \left(t + \color{blue}{y}\right)\right)\right) \]

   6. Applied rewrites 37.8%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]

   7. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{t} \]
   8. Step-by-step derivation

      1. lower-*.f64 17.3

         \[\leadsto b \cdot t \]

   9. Applied rewrites 17.3%

      \[\leadsto b \cdot \color{blue}{t} \]

   if -3.5999999999999999e28 < t < 5.1999999999999995e-150

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 28.2

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

   4. Applied rewrites 28.2%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 11.0%

      \[\leadsto a \]

   if 5.1999999999999995e-150 < t < 9e16

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, \color{blue}{t - 1}, b \cdot \left(2 - t\right)\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - \color{blue}{1}, b \cdot \left(2 - t\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

      6. lower--.f64 70.4

         \[\leadsto \left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right) \]

   6. Applied rewrites 70.4%

      \[\leadsto \color{blue}{\left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right)} \]

   7. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(t - 2\right)} \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(t - \color{blue}{2}\right) \]

      2. lower--.f64 23.4

         \[\leadsto b \cdot \left(t - 2\right) \]

   9. Applied rewrites 23.4%

      \[\leadsto b \cdot \color{blue}{\left(t - 2\right)} \]

   10. Taylor expanded in t around 0

       \[\leadsto b \cdot -2 \]
   11. Step-by-step derivation

   12. Applied rewrites 8.3%

       \[\leadsto b \cdot -2 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 24.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+28}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 1.86:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.6e+28) (* b t) (if (<= t 1.86) a (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.6e+28) {
		tmp = b * t;
	} else if (t <= 1.86) {
		tmp = a;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, 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 (t <= (-3.6d+28)) then
        tmp = b * t
    else if (t <= 1.86d0) then
        tmp = a
    else
        tmp = b * t
    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 (t <= -3.6e+28) {
		tmp = b * t;
	} else if (t <= 1.86) {
		tmp = a;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.6e+28:
		tmp = b * t
	elif t <= 1.86:
		tmp = a
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.6e+28)
		tmp = Float64(b * t);
	elseif (t <= 1.86)
		tmp = a;
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.6e+28)
		tmp = b * t;
	elseif (t <= 1.86)
		tmp = a;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.6e+28], N[(b * t), $MachinePrecision], If[LessEqual[t, 1.86], a, N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.5999999999999999e28 or 1.8600000000000001 < t

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-flip N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-neg-out N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip-rev N/A

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

      15. sub-negate-rev N/A

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

   3. Applied rewrites 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(\left(2 - y\right) - t, b, a \cdot \left(t - 1\right)\right)\right)} \]

   4. Taylor expanded in b around -inf

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

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(2 - \left(t + y\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(2 - \color{blue}{\left(t + y\right)}\right)\right) \]

      4. lower-+.f64 37.8

         \[\leadsto -1 \cdot \left(b \cdot \left(2 - \left(t + \color{blue}{y}\right)\right)\right) \]

   6. Applied rewrites 37.8%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(2 - \left(t + y\right)\right)\right)} \]

   7. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{t} \]
   8. Step-by-step derivation

      1. lower-*.f64 17.3

         \[\leadsto b \cdot t \]

   9. Applied rewrites 17.3%

      \[\leadsto b \cdot \color{blue}{t} \]

   if -3.5999999999999999e28 < t < 1.8600000000000001

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 28.2

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

   4. Applied rewrites 28.2%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 11.0%

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

Alternative 22: 11.0% accurate, 28.4× speedup

Math

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

FPCore

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

C

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

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 = a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := a

Derivation

1. Initial program 95.6%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

2. Taylor expanded in a around inf

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

   1. lower-*.f64 N/A

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

   2. lower--.f64 28.2

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

4. Applied rewrites 28.2%

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

5. Taylor expanded in t around 0

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

7. Applied rewrites 11.0%

   \[\leadsto a \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025149 
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))