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

Percentage Accurate: 95.0% → 97.2%

Time: 5.2s

Alternatives: 23

Speedup: 1.0×

• 36.6% 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: 95.0% 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: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.0%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
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. lift--.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. lift--.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. lift--.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. lift-+.f64 N/A

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

   10. lift--.f64 N/A

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

   11. +-commutative N/A

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

   12. lower-fma.f64 N/A

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

   13. lift--.f64 N/A

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

   14. +-commutative N/A

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

   15. lower-+.f64 N/A

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

   16. *-commutative N/A

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

   17. lower--.f64 N/A

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

3. Applied rewrites 97.2%

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

4. Taylor expanded in a around 0

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

   1. +-commutative N/A

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

   2. negate-sub2 N/A

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

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

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

   4. associate-+r+ N/A

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

   5. lower-+.f64 N/A

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

   6. +-commutative N/A

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

   7. negate-sub2 N/A

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

   8. mul-1-neg N/A

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

   9. *-commutative N/A

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

   10. lower-fma.f64 N/A

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

   11. mul-1-neg N/A

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

   12. negate-sub2 N/A

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

   13. lift--.f64 N/A

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

   14. *-commutative N/A

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

   15. lower-*.f64 N/A

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

   16. lift--.f64 97.2

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

6. Applied rewrites 97.2%

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

Alternative 2: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.0%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
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. lift--.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. lift--.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. lift--.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. lift-+.f64 N/A

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

   10. lift--.f64 N/A

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

   11. +-commutative N/A

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

   12. lower-fma.f64 N/A

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

   13. lift--.f64 N/A

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

   14. +-commutative N/A

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

   15. lower-+.f64 N/A

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

   16. *-commutative N/A

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

   17. lower--.f64 N/A

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

3. Applied rewrites 97.2%

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

Alternative 3: 87.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, z\right)\right) + x\\ \mathbf{if}\;b \leq -9.5 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (fma (- b z) y (fma (- t 2.0) b z)) x)))
   (if (<= b -9.5e-20)
     t_1
     (if (<= b 1.95e+33) (fma (- 1.0 t) a (fma (- 1.0 y) z x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((b - z), y, fma((t - 2.0), b, z)) + x;
	double tmp;
	if (b <= -9.5e-20) {
		tmp = t_1;
	} else if (b <= 1.95e+33) {
		tmp = fma((1.0 - t), a, fma((1.0 - y), z, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(Float64(b - z), y, fma(Float64(t - 2.0), b, z)) + x)
	tmp = 0.0
	if (b <= -9.5e-20)
		tmp = t_1;
	elseif (b <= 1.95e+33)
		tmp = fma(Float64(1.0 - t), a, fma(Float64(1.0 - y), z, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(b - z), $MachinePrecision] * y + N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[b, -9.5e-20], t$95$1, If[LessEqual[b, 1.95e+33], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -9.5e-20 or 1.9500000000000001e33 < b

   1. Initial program 90.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. *-commutative N/A

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

      17. lower--.f64 N/A

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

   3. Applied rewrites 95.0%

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

   4. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. negate-sub2 N/A

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

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

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

      5. +-commutative N/A

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

      6. lower--.f64 N/A

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

   6. Applied rewrites 92.5%

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

   7. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. +-commutative N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lift--.f64 84.4

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

   9. Applied rewrites 84.4%

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

   if -9.5e-20 < b < 1.9500000000000001e33

   1. Initial program 99.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. *-commutative N/A

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

      17. lower--.f64 N/A

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

   3. Applied rewrites 99.2%

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

   4. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. negate-sub2 N/A

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

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

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. associate--l+ N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lower--.f64 N/A

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

      14. *-commutative N/A

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

      15. lift--.f64 N/A

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

      16. lift-*.f64 90.6

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

   6. Applied rewrites 90.6%

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

      1. lift--.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

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

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

      7. negate-sub2 N/A

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

      8. +-commutative N/A

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

      9. +-commutative N/A

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

      10. associate-+l+ N/A

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

      11. negate-sub2 N/A

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

      12. mul-1-neg N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. mul-1-neg N/A

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

      16. negate-sub2 N/A

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

      17. lift--.f64 N/A

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

      18. +-commutative N/A

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

   8. Applied rewrites 90.5%

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

Alternative 4: 84.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) - 2\\ \mathbf{if}\;b \leq -2 \cdot 10^{-16}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, \left(1 - y\right) \cdot z\right)\\ \mathbf{elif}\;b \leq 5.7 \cdot 10^{+87}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ t y) 2.0)))
   (if (<= b -2e-16)
     (fma t_1 b (* (- 1.0 y) z))
     (if (<= b 5.7e+87) (fma (- 1.0 t) a (fma (- 1.0 y) z x)) (fma t_1 b x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) - 2.0;
	double tmp;
	if (b <= -2e-16) {
		tmp = fma(t_1, b, ((1.0 - y) * z));
	} else if (b <= 5.7e+87) {
		tmp = fma((1.0 - t), a, fma((1.0 - y), z, x));
	} else {
		tmp = fma(t_1, b, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) - 2.0)
	tmp = 0.0
	if (b <= -2e-16)
		tmp = fma(t_1, b, Float64(Float64(1.0 - y) * z));
	elseif (b <= 5.7e+87)
		tmp = fma(Float64(1.0 - t), a, fma(Float64(1.0 - y), z, x));
	else
		tmp = fma(t_1, b, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[b, -2e-16], N[(t$95$1 * b + N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.7e+87], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * b + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2e-16

   1. Initial program 91.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. *-commutative N/A

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

      17. lower--.f64 N/A

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. negate-sub2 N/A

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

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

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 76.3

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

   6. Applied rewrites 76.3%

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

   if -2e-16 < b < 5.70000000000000039e87

   1. Initial program 98.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. *-commutative N/A

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

      17. lower--.f64 N/A

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

   3. Applied rewrites 99.2%

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

   4. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. negate-sub2 N/A

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

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

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. associate--l+ N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lower--.f64 N/A

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

      14. *-commutative N/A

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

      15. lift--.f64 N/A

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

      16. lift-*.f64 88.2

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

   6. Applied rewrites 88.2%

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

      1. lift--.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

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

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

      7. negate-sub2 N/A

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

      8. +-commutative N/A

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

      9. +-commutative N/A

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

      10. associate-+l+ N/A

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

      11. negate-sub2 N/A

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

      12. mul-1-neg N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. mul-1-neg N/A

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

      16. negate-sub2 N/A

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

      17. lift--.f64 N/A

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

      18. +-commutative N/A

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

   8. Applied rewrites 88.2%

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

   if 5.70000000000000039e87 < b

   1. Initial program 88.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. *-commutative N/A

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

      17. lower--.f64 N/A

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

   3. Applied rewrites 92.7%

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

   4. Taylor expanded in x around inf

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

      1. +-commutative 81.8

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

      2. negate-sub2 81.8

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

      3. fp-cancel-sub-sign-inv 81.8

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

   6. Applied rewrites 81.8%

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

Alternative 5: 84.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{if}\;b \leq -4 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.7 \cdot 10^{+87}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ t y) 2.0) b x)))
   (if (<= b -4e+43)
     t_1
     (if (<= b 5.7e+87) (fma (- 1.0 t) a (fma (- 1.0 y) z x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((t + y) - 2.0), b, x);
	double tmp;
	if (b <= -4e+43) {
		tmp = t_1;
	} else if (b <= 5.7e+87) {
		tmp = fma((1.0 - t), a, fma((1.0 - y), z, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(t + y) - 2.0), b, x)
	tmp = 0.0
	if (b <= -4e+43)
		tmp = t_1;
	elseif (b <= 5.7e+87)
		tmp = fma(Float64(1.0 - t), a, fma(Float64(1.0 - y), z, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[b, -4e+43], t$95$1, If[LessEqual[b, 5.7e+87], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -4.00000000000000006e43 or 5.70000000000000039e87 < b

   1. Initial program 89.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. *-commutative N/A

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

      17. lower--.f64 N/A

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

   3. Applied rewrites 93.9%

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

   4. Taylor expanded in x around inf

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

      1. +-commutative 80.0

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

      2. negate-sub2 80.0

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

      3. fp-cancel-sub-sign-inv 80.0

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

   6. Applied rewrites 80.0%

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

   if -4.00000000000000006e43 < b < 5.70000000000000039e87

   1. Initial program 98.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. *-commutative N/A

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

      17. lower--.f64 N/A

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

   3. Applied rewrites 99.2%

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

   4. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. negate-sub2 N/A

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

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

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. associate--l+ N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lower--.f64 N/A

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

      14. *-commutative N/A

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

      15. lift--.f64 N/A

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

      16. lift-*.f64 86.9

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

   6. Applied rewrites 86.9%

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

      1. lift--.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

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

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

      7. negate-sub2 N/A

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

      8. +-commutative N/A

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

      9. +-commutative N/A

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

      10. associate-+l+ N/A

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

      11. negate-sub2 N/A

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

      12. mul-1-neg N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. mul-1-neg N/A

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

      16. negate-sub2 N/A

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

      17. lift--.f64 N/A

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

      18. +-commutative N/A

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

   8. Applied rewrites 86.9%

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

Alternative 6: 76.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.22 \cdot 10^{+87}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ t y) 2.0) b x)))
   (if (<= b -1.55e+43)
     t_1
     (if (<= b 1.22e+87) (fma (- 1.0 y) z (- x (* t a))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((t + y) - 2.0), b, x);
	double tmp;
	if (b <= -1.55e+43) {
		tmp = t_1;
	} else if (b <= 1.22e+87) {
		tmp = fma((1.0 - y), z, (x - (t * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(t + y) - 2.0), b, x)
	tmp = 0.0
	if (b <= -1.55e+43)
		tmp = t_1;
	elseif (b <= 1.22e+87)
		tmp = fma(Float64(1.0 - y), z, Float64(x - Float64(t * a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[b, -1.55e+43], t$95$1, If[LessEqual[b, 1.22e+87], N[(N[(1.0 - y), $MachinePrecision] * z + N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.5500000000000001e43 or 1.2200000000000001e87 < b

   1. Initial program 89.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. *-commutative N/A

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

      17. lower--.f64 N/A

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

   3. Applied rewrites 93.9%

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

   4. Taylor expanded in x around inf

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

      1. +-commutative 80.0

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

      2. negate-sub2 80.0

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

      3. fp-cancel-sub-sign-inv 80.0

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

   6. Applied rewrites 80.0%

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

   if -1.5500000000000001e43 < b < 1.2200000000000001e87

   1. Initial program 98.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. *-commutative N/A

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

      17. lower--.f64 N/A

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

   3. Applied rewrites 99.2%

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

   4. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. negate-sub2 N/A

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

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

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. associate--l+ N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lower--.f64 N/A

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

      14. *-commutative N/A

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

      15. lift--.f64 N/A

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

      16. lift-*.f64 86.9

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

   6. Applied rewrites 86.9%

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

   7. Taylor expanded in t around inf

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

   9. Applied rewrites 74.7%

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

Alternative 7: 70.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{if}\;b \leq -3.9 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+87}:\\ \;\;\;\;\left(z + x\right) - a \cdot \left(t - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ t y) 2.0) b x)))
   (if (<= b -3.9e-19)
     t_1
     (if (<= b 1.2e+87) (- (+ z x) (* 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 + y) - 2.0), b, x);
	double tmp;
	if (b <= -3.9e-19) {
		tmp = t_1;
	} else if (b <= 1.2e+87) {
		tmp = (z + x) - (a * (t - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(t + y) - 2.0), b, x)
	tmp = 0.0
	if (b <= -3.9e-19)
		tmp = t_1;
	elseif (b <= 1.2e+87)
		tmp = Float64(Float64(z + x) - 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[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[b, -3.9e-19], t$95$1, If[LessEqual[b, 1.2e+87], N[(N[(z + x), $MachinePrecision] - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.89999999999999995e-19 or 1.19999999999999991e87 < b

   1. Initial program 90.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. *-commutative N/A

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

      17. lower--.f64 N/A

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

   3. Applied rewrites 94.6%

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

   4. Taylor expanded in x around inf

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

      1. +-commutative 76.2

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

      2. negate-sub2 76.2

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

      3. fp-cancel-sub-sign-inv 76.2

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

   6. Applied rewrites 76.2%

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

   if -3.89999999999999995e-19 < b < 1.19999999999999991e87

   1. Initial program 98.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. *-commutative N/A

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

      17. lower--.f64 N/A

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

   3. Applied rewrites 99.2%

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

   4. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. negate-sub2 N/A

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

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

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. associate--l+ N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lower--.f64 N/A

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

      14. *-commutative N/A

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

      15. lift--.f64 N/A

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

      16. lift-*.f64 88.3

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

   6. Applied rewrites 88.3%

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

   7. Taylor expanded in y around 0

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

      1. associate-+r- N/A

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

      2. *-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. negate-sub2 N/A

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

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

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

      7. lower--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lift--.f64 66.8

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

   9. Applied rewrites 66.8%

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

Alternative 8: 64.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ t y) 2.0) b x)))
   (if (<= b -2.6e-19) t_1 (if (<= b 5.6e+33) (fma (- 1.0 t) a x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((t + y) - 2.0), b, x);
	double tmp;
	if (b <= -2.6e-19) {
		tmp = t_1;
	} else if (b <= 5.6e+33) {
		tmp = fma((1.0 - t), a, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(t + y) - 2.0), b, x)
	tmp = 0.0
	if (b <= -2.6e-19)
		tmp = t_1;
	elseif (b <= 5.6e+33)
		tmp = fma(Float64(1.0 - t), a, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[b, -2.6e-19], t$95$1, If[LessEqual[b, 5.6e+33], N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.60000000000000013e-19 or 5.6000000000000002e33 < b

   1. Initial program 90.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. *-commutative N/A

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

      17. lower--.f64 N/A

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

   3. Applied rewrites 95.0%

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

   4. Taylor expanded in x around inf

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

      1. +-commutative 74.5

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

      2. negate-sub2 74.5

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

      3. fp-cancel-sub-sign-inv 74.5

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

   6. Applied rewrites 74.5%

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

   if -2.60000000000000013e-19 < b < 5.6000000000000002e33

   1. Initial program 99.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. *-commutative N/A

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

      17. lower--.f64 N/A

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

   3. Applied rewrites 99.2%

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

   4. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. negate-sub2 N/A

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

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

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. associate--l+ N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lower--.f64 N/A

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

      14. *-commutative N/A

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

      15. lift--.f64 N/A

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

      16. lift-*.f64 90.6

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

   6. Applied rewrites 90.6%

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

   7. Taylor expanded in t around inf

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

   9. Applied rewrites 77.9%

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

   10. Taylor expanded in z around 0

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

       1. *-commutative N/A

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

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

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

       3. mul-1-neg N/A

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

       4. *-commutative N/A

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

       5. mul-1-neg N/A

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

       6. negate-sub2 N/A

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

       7. +-commutative N/A

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

       8. negate-sub2 N/A

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

       9. mul-1-neg N/A

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

       10. *-commutative N/A

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

       11. lower-fma.f64 N/A

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

       12. mul-1-neg N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\left(t - 1\right)\right), a, x\right) \]

       13. negate-sub2 N/A

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

       14. lift--.f64 56.0

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

   12. Applied rewrites 56.0%

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

Alternative 9: 61.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.45 \cdot 10^{+87}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -2e-16) t_1 (if (<= b 2.45e+87) (fma (- 1.0 t) a x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -2e-16) {
		tmp = t_1;
	} else if (b <= 2.45e+87) {
		tmp = fma((1.0 - t), a, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -2e-16)
		tmp = t_1;
	elseif (b <= 2.45e+87)
		tmp = fma(Float64(1.0 - t), a, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2e-16], t$95$1, If[LessEqual[b, 2.45e+87], N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2e-16 or 2.44999999999999986e87 < b

   1. Initial program 90.1%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 69.9

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 69.9

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

   4. Applied rewrites 69.9%

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

   if -2e-16 < b < 2.44999999999999986e87

   1. Initial program 98.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. *-commutative N/A

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

      17. lower--.f64 N/A

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

   3. Applied rewrites 99.2%

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

   4. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. negate-sub2 N/A

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

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

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. associate--l+ N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lower--.f64 N/A

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

      14. *-commutative N/A

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

      15. lift--.f64 N/A

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

      16. lift-*.f64 88.2

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

   6. Applied rewrites 88.2%

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

   7. Taylor expanded in t around inf

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

   9. Applied rewrites 76.0%

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

   10. Taylor expanded in z around 0

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

       1. *-commutative N/A

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

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

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

       3. mul-1-neg N/A

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

       4. *-commutative N/A

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

       5. mul-1-neg N/A

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

       6. negate-sub2 N/A

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

       7. +-commutative N/A

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

       8. negate-sub2 N/A

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

       9. mul-1-neg N/A

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

       10. *-commutative N/A

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

       11. lower-fma.f64 N/A

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

       12. mul-1-neg N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\left(t - 1\right)\right), a, x\right) \]

       13. negate-sub2 N/A

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

       14. lift--.f64 54.4

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

   12. Applied rewrites 54.4%

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

Alternative 10: 57.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -4.7 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+26}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -4.7e+61) t_1 (if (<= t 2.65e+26) (fma (- y 2.0) b x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -4.7e+61) {
		tmp = t_1;
	} else if (t <= 2.65e+26) {
		tmp = fma((y - 2.0), b, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -4.7e+61)
		tmp = t_1;
	elseif (t <= 2.65e+26)
		tmp = fma(Float64(y - 2.0), b, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -4.7e+61], t$95$1, If[LessEqual[t, 2.65e+26], N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.6999999999999998e61 or 2.64999999999999984e26 < t

   1. Initial program 91.6%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 67.8

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

   4. Applied rewrites 67.8%

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

   if -4.6999999999999998e61 < t < 2.64999999999999984e26

   1. Initial program 97.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. *-commutative N/A

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

      17. lower--.f64 N/A

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

   3. Applied rewrites 98.7%

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

   4. Taylor expanded in x around inf

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

      1. +-commutative 52.2

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

      2. negate-sub2 52.2

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

      3. fp-cancel-sub-sign-inv 52.2

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

   6. Applied rewrites 52.2%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{y} - 2, b, x\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 50.0%

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

Alternative 11: 56.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1020000000:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 y) z x)))
   (if (<= z -6.2e+113) t_1 (if (<= z 1020000000.0) (fma (- 1.0 t) a x) 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);
	double tmp;
	if (z <= -6.2e+113) {
		tmp = t_1;
	} else if (z <= 1020000000.0) {
		tmp = fma((1.0 - t), a, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - y), z, x)
	tmp = 0.0
	if (z <= -6.2e+113)
		tmp = t_1;
	elseif (z <= 1020000000.0)
		tmp = fma(Float64(1.0 - t), a, x);
	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 + x), $MachinePrecision]}, If[LessEqual[z, -6.2e+113], t$95$1, If[LessEqual[z, 1020000000.0], N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.19999999999999982e113 or 1.02e9 < z

   1. Initial program 91.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. *-commutative N/A

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

      17. lower--.f64 N/A

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

   3. Applied rewrites 94.9%

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

   4. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. negate-sub2 N/A

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

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

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. associate--l+ N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lower--.f64 N/A

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

      14. *-commutative N/A

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

      15. lift--.f64 N/A

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

      16. lift-*.f64 78.0

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

   6. Applied rewrites 78.0%

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

   7. Taylor expanded in t around inf

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

   9. Applied rewrites 73.4%

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

   10. Taylor expanded in x around inf

       \[\leadsto \mathsf{fma}\left(1 - y, z, x\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 62.7%

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

   if -6.19999999999999982e113 < z < 1.02e9

   1. Initial program 97.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. *-commutative N/A

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

      17. lower--.f64 N/A

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

   3. Applied rewrites 98.7%

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

   4. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. negate-sub2 N/A

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

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

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. associate--l+ N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lower--.f64 N/A

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

      14. *-commutative N/A

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

      15. lift--.f64 N/A

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

      16. lift-*.f64 59.9

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

   6. Applied rewrites 59.9%

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

   7. Taylor expanded in t around inf

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

   9. Applied rewrites 48.0%

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

   10. Taylor expanded in z around 0

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

       1. *-commutative N/A

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

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

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

       3. mul-1-neg N/A

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

       4. *-commutative N/A

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

       5. mul-1-neg N/A

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

       6. negate-sub2 N/A

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

       7. +-commutative N/A

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

       8. negate-sub2 N/A

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

       9. mul-1-neg N/A

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

       10. *-commutative N/A

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

       11. lower-fma.f64 N/A

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

       12. mul-1-neg N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\left(t - 1\right)\right), a, x\right) \]

       13. negate-sub2 N/A

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

       14. lift--.f64 51.8

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

   12. Applied rewrites 51.8%

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

Alternative 12: 53.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+157}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 y) z)))
   (if (<= z -1.1e+131) t_1 (if (<= z 8e+157) (fma (- 1.0 t) a x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double tmp;
	if (z <= -1.1e+131) {
		tmp = t_1;
	} else if (z <= 8e+157) {
		tmp = fma((1.0 - t), a, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (z <= -1.1e+131)
		tmp = t_1;
	elseif (z <= 8e+157)
		tmp = fma(Float64(1.0 - t), a, x);
	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), $MachinePrecision]}, If[LessEqual[z, -1.1e+131], t$95$1, If[LessEqual[z, 8e+157], N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0999999999999999e131 or 7.99999999999999987e157 < z

   1. Initial program 90.1%

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

   2. Taylor expanded in z around inf

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

      1. negate-sub2 N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. negate-sub2 N/A

         \[\leadsto \left(1 - y\right) \cdot z \]

      7. lower--.f64 67.1

         \[\leadsto \left(1 - y\right) \cdot z \]

   4. Applied rewrites 67.1%

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

   if -1.0999999999999999e131 < z < 7.99999999999999987e157

   1. Initial program 96.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. *-commutative N/A

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

      17. lower--.f64 N/A

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

   3. Applied rewrites 98.1%

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

   4. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. negate-sub2 N/A

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

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

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. associate--l+ N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lower--.f64 N/A

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

      14. *-commutative N/A

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

      15. lift--.f64 N/A

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

      16. lift-*.f64 61.3

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

   6. Applied rewrites 61.3%

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

   7. Taylor expanded in t around inf

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

   9. Applied rewrites 50.2%

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

   10. Taylor expanded in z around 0

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

       1. *-commutative N/A

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

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

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

       3. mul-1-neg N/A

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

       4. *-commutative N/A

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

       5. mul-1-neg N/A

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

       6. negate-sub2 N/A

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

       7. +-commutative N/A

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

       8. negate-sub2 N/A

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

       9. mul-1-neg N/A

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

       10. *-commutative N/A

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

       11. lower-fma.f64 N/A

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

       12. mul-1-neg N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\left(t - 1\right)\right), a, x\right) \]

       13. negate-sub2 N/A

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

       14. lift--.f64 48.9

           \[\leadsto \mathsf{fma}\left(1 - t, a, x\right) \]

   12. Applied rewrites 48.9%

       \[\leadsto \mathsf{fma}\left(1 - t, \color{blue}{a}, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 50.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -2.45 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{-26}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+26}:\\ \;\;\;\;x - \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -2.45e+29)
     t_1
     (if (<= t -1.22e-26) (* (- b z) y) (if (<= t 1.9e+26) (- x (- a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -2.45e+29) {
		tmp = t_1;
	} else if (t <= -1.22e-26) {
		tmp = (b - z) * y;
	} else if (t <= 1.9e+26) {
		tmp = x - -a;
	} 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 = (b - a) * t
    if (t <= (-2.45d+29)) then
        tmp = t_1
    else if (t <= (-1.22d-26)) then
        tmp = (b - z) * y
    else if (t <= 1.9d+26) then
        tmp = x - -a
    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 = (b - a) * t;
	double tmp;
	if (t <= -2.45e+29) {
		tmp = t_1;
	} else if (t <= -1.22e-26) {
		tmp = (b - z) * y;
	} else if (t <= 1.9e+26) {
		tmp = x - -a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -2.45e+29:
		tmp = t_1
	elif t <= -1.22e-26:
		tmp = (b - z) * y
	elif t <= 1.9e+26:
		tmp = x - -a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -2.45e+29)
		tmp = t_1;
	elseif (t <= -1.22e-26)
		tmp = Float64(Float64(b - z) * y);
	elseif (t <= 1.9e+26)
		tmp = Float64(x - Float64(-a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	tmp = 0.0;
	if (t <= -2.45e+29)
		tmp = t_1;
	elseif (t <= -1.22e-26)
		tmp = (b - z) * y;
	elseif (t <= 1.9e+26)
		tmp = x - -a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -2.45e+29], t$95$1, If[LessEqual[t, -1.22e-26], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 1.9e+26], N[(x - (-a)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4500000000000001e29 or 1.9000000000000001e26 < t

   1. Initial program 92.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b - a\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b - a\right) \cdot \color{blue}{t} \]

      3. lower--.f64 66.4

         \[\leadsto \left(b - a\right) \cdot t \]

   4. Applied rewrites 66.4%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   if -2.4500000000000001e29 < t < -1.22e-26

   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. *-commutative N/A

         \[\leadsto \left(b - z\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b - z\right) \cdot \color{blue}{y} \]

      3. lower--.f64 38.8

         \[\leadsto \left(b - z\right) \cdot y \]

   4. Applied rewrites 38.8%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   if -1.22e-26 < t < 1.9000000000000001e26

   1. Initial program 97.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(\left(t + y\right) - 2\right) + z \cdot \left(1 - y\right)\right)\right) - a \cdot \left(t - 1\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(x + \left(b \cdot \left(\left(t + y\right) - 2\right) + z \cdot \left(1 - y\right)\right)\right) - \color{blue}{a \cdot \left(t - 1\right)} \]

   4. Applied rewrites 98.9%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in x around inf

      \[\leadsto x - \color{blue}{\left(t - 1\right)} \cdot a \]
   6. Step-by-step derivation

   7. Applied rewrites 37.7%

      \[\leadsto x - \color{blue}{\left(t - 1\right)} \cdot a \]

   8. Taylor expanded in t around 0

      \[\leadsto x - -1 \cdot \color{blue}{a} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(a\right)\right) \]

      2. lower-neg.f64 36.3

         \[\leadsto x - \left(-a\right) \]

   10. Applied rewrites 36.3%

       \[\leadsto x - \left(-a\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 49.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -1.95 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-23}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+26}:\\ \;\;\;\;x - \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -1.95e+28)
     t_1
     (if (<= t -1.9e-23)
       (* (- 1.0 y) z)
       (if (<= t 1.9e+26) (- x (- a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -1.95e+28) {
		tmp = t_1;
	} else if (t <= -1.9e-23) {
		tmp = (1.0 - y) * z;
	} else if (t <= 1.9e+26) {
		tmp = x - -a;
	} 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 = (b - a) * t
    if (t <= (-1.95d+28)) then
        tmp = t_1
    else if (t <= (-1.9d-23)) then
        tmp = (1.0d0 - y) * z
    else if (t <= 1.9d+26) then
        tmp = x - -a
    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 = (b - a) * t;
	double tmp;
	if (t <= -1.95e+28) {
		tmp = t_1;
	} else if (t <= -1.9e-23) {
		tmp = (1.0 - y) * z;
	} else if (t <= 1.9e+26) {
		tmp = x - -a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -1.95e+28:
		tmp = t_1
	elif t <= -1.9e-23:
		tmp = (1.0 - y) * z
	elif t <= 1.9e+26:
		tmp = x - -a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -1.95e+28)
		tmp = t_1;
	elseif (t <= -1.9e-23)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (t <= 1.9e+26)
		tmp = Float64(x - Float64(-a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	tmp = 0.0;
	if (t <= -1.95e+28)
		tmp = t_1;
	elseif (t <= -1.9e-23)
		tmp = (1.0 - y) * z;
	elseif (t <= 1.9e+26)
		tmp = x - -a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.95e+28], t$95$1, If[LessEqual[t, -1.9e-23], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t, 1.9e+26], N[(x - (-a)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9499999999999999e28 or 1.9000000000000001e26 < t

   1. Initial program 92.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b - a\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b - a\right) \cdot \color{blue}{t} \]

      3. lower--.f64 66.4

         \[\leadsto \left(b - a\right) \cdot t \]

   4. Applied rewrites 66.4%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   if -1.9499999999999999e28 < t < -1.90000000000000006e-23

   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. negate-sub2 N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

      2. mul-1-neg N/A

         \[\leadsto z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(y - 1\right)\right) \cdot \color{blue}{z} \]

      4. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(y - 1\right)\right) \cdot \color{blue}{z} \]

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \cdot z \]

      6. negate-sub2 N/A

         \[\leadsto \left(1 - y\right) \cdot z \]

      7. lower--.f64 32.9

         \[\leadsto \left(1 - y\right) \cdot z \]

   4. Applied rewrites 32.9%

      \[\leadsto \color{blue}{\left(1 - y\right) \cdot z} \]

   if -1.90000000000000006e-23 < t < 1.9000000000000001e26

   1. Initial program 97.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(\left(t + y\right) - 2\right) + z \cdot \left(1 - y\right)\right)\right) - a \cdot \left(t - 1\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(x + \left(b \cdot \left(\left(t + y\right) - 2\right) + z \cdot \left(1 - y\right)\right)\right) - \color{blue}{a \cdot \left(t - 1\right)} \]

   4. Applied rewrites 98.9%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in x around inf

      \[\leadsto x - \color{blue}{\left(t - 1\right)} \cdot a \]
   6. Step-by-step derivation

   7. Applied rewrites 37.7%

      \[\leadsto x - \color{blue}{\left(t - 1\right)} \cdot a \]

   8. Taylor expanded in t around 0

      \[\leadsto x - -1 \cdot \color{blue}{a} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(a\right)\right) \]

      2. lower-neg.f64 36.3

         \[\leadsto x - \left(-a\right) \]

   10. Applied rewrites 36.3%

       \[\leadsto x - \left(-a\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 46.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;z \leq -7.7 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-281}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-178}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+189}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 y) z)))
   (if (<= z -7.7e+130)
     t_1
     (if (<= z 7.5e-281)
       (fma t b x)
       (if (<= z 8.5e-178)
         (* (- 1.0 t) a)
         (if (<= z 1.9e+189) (fma t b x) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double tmp;
	if (z <= -7.7e+130) {
		tmp = t_1;
	} else if (z <= 7.5e-281) {
		tmp = fma(t, b, x);
	} else if (z <= 8.5e-178) {
		tmp = (1.0 - t) * a;
	} else if (z <= 1.9e+189) {
		tmp = fma(t, b, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (z <= -7.7e+130)
		tmp = t_1;
	elseif (z <= 7.5e-281)
		tmp = fma(t, b, x);
	elseif (z <= 8.5e-178)
		tmp = Float64(Float64(1.0 - t) * a);
	elseif (z <= 1.9e+189)
		tmp = fma(t, b, x);
	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), $MachinePrecision]}, If[LessEqual[z, -7.7e+130], t$95$1, If[LessEqual[z, 7.5e-281], N[(t * b + x), $MachinePrecision], If[LessEqual[z, 8.5e-178], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[z, 1.9e+189], N[(t * b + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.7000000000000004e130 or 1.8999999999999999e189 < z

   1. Initial program 90.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
   3. Step-by-step derivation

      1. negate-sub2 N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

      2. mul-1-neg N/A

         \[\leadsto z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(y - 1\right)\right) \cdot \color{blue}{z} \]

      4. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(y - 1\right)\right) \cdot \color{blue}{z} \]

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \cdot z \]

      6. negate-sub2 N/A

         \[\leadsto \left(1 - y\right) \cdot z \]

      7. lower--.f64 68.5

         \[\leadsto \left(1 - y\right) \cdot z \]

   4. Applied rewrites 68.5%

      \[\leadsto \color{blue}{\left(1 - y\right) \cdot z} \]

   if -7.7000000000000004e130 < z < 7.49999999999999968e-281 or 8.5000000000000001e-178 < z < 1.8999999999999999e189

   1. Initial program 96.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. lift--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      5. lift--.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right)} \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right) \cdot a}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right)} \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

      9. lift-+.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      10. lift--.f64 N/A

          \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right)} \cdot b \]

      11. +-commutative N/A

          \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      12. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      13. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + t\right) - 2}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      15. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{a \cdot \left(t - 1\right)}\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - a \cdot \left(t - 1\right)}\right) \]

   3. Applied rewrites 97.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(1 - y, z, x\right) - \left(t - 1\right) \cdot a\right)} \]

   4. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{x}\right) \]
   5. Step-by-step derivation

      1. +-commutative 58.0

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) \]

      2. negate-sub2 58.0

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) \]

      3. fp-cancel-sub-sign-inv 58.0

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) \]

   6. Applied rewrites 58.0%

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{x}\right) \]

   7. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{t}, b, x\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 35.1%

      \[\leadsto \mathsf{fma}\left(\color{blue}{t}, b, x\right) \]

   if 7.49999999999999968e-281 < z < 8.5000000000000001e-178

   1. Initial program 96.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
   3. Step-by-step derivation

      1. negate-sub2 N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

         \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(t - 1\right)\right) \cdot \color{blue}{a} \]

      4. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(t - 1\right)\right) \cdot \color{blue}{a} \]

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. negate-sub2 N/A

         \[\leadsto \left(1 - t\right) \cdot a \]

      7. lower--.f64 37.5

         \[\leadsto \left(1 - t\right) \cdot a \]

   4. Applied rewrites 37.5%

      \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 43.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - t\right) \cdot a\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+73}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 t) a)))
   (if (<= a -6.2e+17) t_1 (if (<= a 1.6e+73) (fma t b x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - t) * a;
	double tmp;
	if (a <= -6.2e+17) {
		tmp = t_1;
	} else if (a <= 1.6e+73) {
		tmp = fma(t, b, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - t) * a)
	tmp = 0.0
	if (a <= -6.2e+17)
		tmp = t_1;
	elseif (a <= 1.6e+73)
		tmp = fma(t, b, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -6.2e+17], t$95$1, If[LessEqual[a, 1.6e+73], N[(t * b + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -6.2e17 or 1.59999999999999991e73 < a

   1. Initial program 91.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
   3. Step-by-step derivation

      1. negate-sub2 N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

         \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(t - 1\right)\right) \cdot \color{blue}{a} \]

      4. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(t - 1\right)\right) \cdot \color{blue}{a} \]

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. negate-sub2 N/A

         \[\leadsto \left(1 - t\right) \cdot a \]

      7. lower--.f64 54.2

         \[\leadsto \left(1 - t\right) \cdot a \]

   4. Applied rewrites 54.2%

      \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

   if -6.2e17 < a < 1.59999999999999991e73

   1. Initial program 97.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. lift--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      5. lift--.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right)} \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right) \cdot a}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right)} \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

      9. lift-+.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      10. lift--.f64 N/A

          \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right)} \cdot b \]

      11. +-commutative N/A

          \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      12. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      13. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + t\right) - 2}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      15. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{a \cdot \left(t - 1\right)}\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - a \cdot \left(t - 1\right)}\right) \]

   3. Applied rewrites 98.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(1 - y, z, x\right) - \left(t - 1\right) \cdot a\right)} \]

   4. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{x}\right) \]
   5. Step-by-step derivation

      1. +-commutative 62.9

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) \]

      2. negate-sub2 62.9

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) \]

      3. fp-cancel-sub-sign-inv 62.9

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) \]

   6. Applied rewrites 62.9%

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{x}\right) \]

   7. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{t}, b, x\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 40.0%

      \[\leadsto \mathsf{fma}\left(\color{blue}{t}, b, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 39.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+128}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.3e+128) (* b y) (if (<= y 6.5e+32) (fma t b x) (* (- z) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.3e+128) {
		tmp = b * y;
	} else if (y <= 6.5e+32) {
		tmp = fma(t, b, x);
	} else {
		tmp = -z * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.3e+128)
		tmp = Float64(b * y);
	elseif (y <= 6.5e+32)
		tmp = fma(t, b, x);
	else
		tmp = Float64(Float64(-z) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.3e+128], N[(b * y), $MachinePrecision], If[LessEqual[y, 6.5e+32], N[(t * b + x), $MachinePrecision], N[((-z) * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.29999999999999998e128

   1. Initial program 88.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b - z\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b - z\right) \cdot \color{blue}{y} \]

      3. lower--.f64 77.7

         \[\leadsto \left(b - z\right) \cdot y \]

   4. Applied rewrites 77.7%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   5. Taylor expanded in z around 0

      \[\leadsto b \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 41.5%

      \[\leadsto b \cdot y \]

   if -2.29999999999999998e128 < y < 6.4999999999999994e32

   1. Initial program 97.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. lift--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      5. lift--.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right)} \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right) \cdot a}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right)} \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

      9. lift-+.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      10. lift--.f64 N/A

          \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right)} \cdot b \]

      11. +-commutative N/A

          \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      12. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      13. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + t\right) - 2}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      15. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{a \cdot \left(t - 1\right)}\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - a \cdot \left(t - 1\right)}\right) \]

   3. Applied rewrites 98.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(1 - y, z, x\right) - \left(t - 1\right) \cdot a\right)} \]

   4. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{x}\right) \]
   5. Step-by-step derivation

      1. +-commutative 52.0

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) \]

      2. negate-sub2 52.0

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) \]

      3. fp-cancel-sub-sign-inv 52.0

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) \]

   6. Applied rewrites 52.0%

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{x}\right) \]

   7. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{t}, b, x\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 38.8%

      \[\leadsto \mathsf{fma}\left(\color{blue}{t}, b, x\right) \]

   if 6.4999999999999994e32 < y

   1. Initial program 91.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b - z\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b - z\right) \cdot \color{blue}{y} \]

      3. lower--.f64 68.3

         \[\leadsto \left(b - z\right) \cdot y \]

   4. Applied rewrites 68.3%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   5. Taylor expanded in z around inf

      \[\leadsto \left(-1 \cdot z\right) \cdot y \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(z\right)\right) \cdot y \]

      2. lower-neg.f64 38.4

         \[\leadsto \left(-z\right) \cdot y \]

   7. Applied rewrites 38.4%

      \[\leadsto \left(-z\right) \cdot y \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 36.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+66}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+26}:\\ \;\;\;\;x - \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.1e+66) (* b t) (if (<= t 5.8e+26) (- x (- a)) (* (- a) t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.1e+66) {
		tmp = b * t;
	} else if (t <= 5.8e+26) {
		tmp = x - -a;
	} else {
		tmp = -a * 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 <= (-4.1d+66)) then
        tmp = b * t
    else if (t <= 5.8d+26) then
        tmp = x - -a
    else
        tmp = -a * 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 <= -4.1e+66) {
		tmp = b * t;
	} else if (t <= 5.8e+26) {
		tmp = x - -a;
	} else {
		tmp = -a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.1e+66:
		tmp = b * t
	elif t <= 5.8e+26:
		tmp = x - -a
	else:
		tmp = -a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.1e+66)
		tmp = Float64(b * t);
	elseif (t <= 5.8e+26)
		tmp = Float64(x - Float64(-a));
	else
		tmp = Float64(Float64(-a) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.1e+66)
		tmp = b * t;
	elseif (t <= 5.8e+26)
		tmp = x - -a;
	else
		tmp = -a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.1e+66], N[(b * t), $MachinePrecision], If[LessEqual[t, 5.8e+26], N[(x - (-a)), $MachinePrecision], N[((-a) * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.09999999999999994e66

   1. Initial program 91.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b - a\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b - a\right) \cdot \color{blue}{t} \]

      3. lower--.f64 69.8

         \[\leadsto \left(b - a\right) \cdot t \]

   4. Applied rewrites 69.8%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   5. Taylor expanded in a around 0

      \[\leadsto b \cdot t \]
   6. Step-by-step derivation

   7. Applied rewrites 37.7%

      \[\leadsto b \cdot t \]

   if -4.09999999999999994e66 < t < 5.8e26

   1. Initial program 97.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(\left(t + y\right) - 2\right) + z \cdot \left(1 - y\right)\right)\right) - a \cdot \left(t - 1\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(x + \left(b \cdot \left(\left(t + y\right) - 2\right) + z \cdot \left(1 - y\right)\right)\right) - \color{blue}{a \cdot \left(t - 1\right)} \]

   4. Applied rewrites 98.8%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in x around inf

      \[\leadsto x - \color{blue}{\left(t - 1\right)} \cdot a \]
   6. Step-by-step derivation

   7. Applied rewrites 37.7%

      \[\leadsto x - \color{blue}{\left(t - 1\right)} \cdot a \]

   8. Taylor expanded in t around 0

      \[\leadsto x - -1 \cdot \color{blue}{a} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(a\right)\right) \]

      2. lower-neg.f64 34.5

         \[\leadsto x - \left(-a\right) \]

   10. Applied rewrites 34.5%

       \[\leadsto x - \left(-a\right) \]

   if 5.8e26 < t

   1. Initial program 91.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b - a\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b - a\right) \cdot \color{blue}{t} \]

      3. lower--.f64 66.5

         \[\leadsto \left(b - a\right) \cdot t \]

   4. Applied rewrites 66.5%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   5. Taylor expanded in a around inf

      \[\leadsto \left(-1 \cdot a\right) \cdot t \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(a\right)\right) \cdot t \]

      2. lower-neg.f64 38.2

         \[\leadsto \left(-a\right) \cdot t \]

   7. Applied rewrites 38.2%

      \[\leadsto \left(-a\right) \cdot t \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 34.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+66}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+65}:\\ \;\;\;\;x - \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.1e+66) (* b t) (if (<= t 8.5e+65) (- x (- a)) (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.1e+66) {
		tmp = b * t;
	} else if (t <= 8.5e+65) {
		tmp = x - -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 <= (-4.1d+66)) then
        tmp = b * t
    else if (t <= 8.5d+65) then
        tmp = x - -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 <= -4.1e+66) {
		tmp = b * t;
	} else if (t <= 8.5e+65) {
		tmp = x - -a;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.1e+66:
		tmp = b * t
	elif t <= 8.5e+65:
		tmp = x - -a
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.1e+66)
		tmp = Float64(b * t);
	elseif (t <= 8.5e+65)
		tmp = Float64(x - Float64(-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 <= -4.1e+66)
		tmp = b * t;
	elseif (t <= 8.5e+65)
		tmp = x - -a;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.1e+66], N[(b * t), $MachinePrecision], If[LessEqual[t, 8.5e+65], N[(x - (-a)), $MachinePrecision], N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.09999999999999994e66 or 8.50000000000000075e65 < t

   1. Initial program 91.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b - a\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b - a\right) \cdot \color{blue}{t} \]

      3. lower--.f64 69.7

         \[\leadsto \left(b - a\right) \cdot t \]

   4. Applied rewrites 69.7%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   5. Taylor expanded in a around 0

      \[\leadsto b \cdot t \]
   6. Step-by-step derivation

   7. Applied rewrites 37.2%

      \[\leadsto b \cdot t \]

   if -4.09999999999999994e66 < t < 8.50000000000000075e65

   1. Initial program 97.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(\left(t + y\right) - 2\right) + z \cdot \left(1 - y\right)\right)\right) - a \cdot \left(t - 1\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(x + \left(b \cdot \left(\left(t + y\right) - 2\right) + z \cdot \left(1 - y\right)\right)\right) - \color{blue}{a \cdot \left(t - 1\right)} \]

   4. Applied rewrites 98.8%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in x around inf

      \[\leadsto x - \color{blue}{\left(t - 1\right)} \cdot a \]
   6. Step-by-step derivation

   7. Applied rewrites 37.8%

      \[\leadsto x - \color{blue}{\left(t - 1\right)} \cdot a \]

   8. Taylor expanded in t around 0

      \[\leadsto x - -1 \cdot \color{blue}{a} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(a\right)\right) \]

      2. lower-neg.f64 33.4

         \[\leadsto x - \left(-a\right) \]

   10. Applied rewrites 33.4%

       \[\leadsto x - \left(-a\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 26.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+47}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq -1.38 \cdot 10^{-244}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.8e+47)
   (* b t)
   (if (<= t -1.38e-244) (* b y) (if (<= t 1.25e+71) x (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.8e+47) {
		tmp = b * t;
	} else if (t <= -1.38e-244) {
		tmp = b * y;
	} else if (t <= 1.25e+71) {
		tmp = x;
	} 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 <= (-2.8d+47)) then
        tmp = b * t
    else if (t <= (-1.38d-244)) then
        tmp = b * y
    else if (t <= 1.25d+71) then
        tmp = x
    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 <= -2.8e+47) {
		tmp = b * t;
	} else if (t <= -1.38e-244) {
		tmp = b * y;
	} else if (t <= 1.25e+71) {
		tmp = x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.8e+47:
		tmp = b * t
	elif t <= -1.38e-244:
		tmp = b * y
	elif t <= 1.25e+71:
		tmp = x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.8e+47)
		tmp = Float64(b * t);
	elseif (t <= -1.38e-244)
		tmp = Float64(b * y);
	elseif (t <= 1.25e+71)
		tmp = x;
	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 <= -2.8e+47)
		tmp = b * t;
	elseif (t <= -1.38e-244)
		tmp = b * y;
	elseif (t <= 1.25e+71)
		tmp = x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.8e+47], N[(b * t), $MachinePrecision], If[LessEqual[t, -1.38e-244], N[(b * y), $MachinePrecision], If[LessEqual[t, 1.25e+71], x, N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.79999999999999988e47 or 1.24999999999999993e71 < t

   1. Initial program 91.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b - a\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b - a\right) \cdot \color{blue}{t} \]

      3. lower--.f64 69.1

         \[\leadsto \left(b - a\right) \cdot t \]

   4. Applied rewrites 69.1%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   5. Taylor expanded in a around 0

      \[\leadsto b \cdot t \]
   6. Step-by-step derivation

   7. Applied rewrites 36.8%

      \[\leadsto b \cdot t \]

   if -2.79999999999999988e47 < t < -1.3799999999999999e-244

   1. Initial program 97.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b - z\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b - z\right) \cdot \color{blue}{y} \]

      3. lower--.f64 39.1

         \[\leadsto \left(b - z\right) \cdot y \]

   4. Applied rewrites 39.1%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   5. Taylor expanded in z around 0

      \[\leadsto b \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 21.8%

      \[\leadsto b \cdot y \]

   if -1.3799999999999999e-244 < t < 1.24999999999999993e71

   1. Initial program 97.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 17.9%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 24.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+105}:\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.8e+119) x (if (<= x 4.3e+105) (* b t) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.8e+119) {
		tmp = x;
	} else if (x <= 4.3e+105) {
		tmp = b * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, 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 (x <= (-4.8d+119)) then
        tmp = x
    else if (x <= 4.3d+105) then
        tmp = b * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.8e+119) {
		tmp = x;
	} else if (x <= 4.3e+105) {
		tmp = b * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.8e+119:
		tmp = x
	elif x <= 4.3e+105:
		tmp = b * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.8e+119)
		tmp = x;
	elseif (x <= 4.3e+105)
		tmp = Float64(b * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -4.8e+119)
		tmp = x;
	elseif (x <= 4.3e+105)
		tmp = b * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.8e+119], x, If[LessEqual[x, 4.3e+105], N[(b * t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.8e119 or 4.3000000000000002e105 < x

   1. Initial program 94.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 37.4%

      \[\leadsto \color{blue}{x} \]

   if -4.8e119 < x < 4.3000000000000002e105

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b - a\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b - a\right) \cdot \color{blue}{t} \]

      3. lower--.f64 35.9

         \[\leadsto \left(b - a\right) \cdot t \]

   4. Applied rewrites 35.9%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   5. Taylor expanded in a around 0

      \[\leadsto b \cdot t \]
   6. Step-by-step derivation

   7. Applied rewrites 19.2%

      \[\leadsto b \cdot t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 20.5% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+109}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.4e+106) x (if (<= x 5.6e+109) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.4e+106) {
		tmp = x;
	} else if (x <= 5.6e+109) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, 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 (x <= (-6.4d+106)) then
        tmp = x
    else if (x <= 5.6d+109) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.4e+106) {
		tmp = x;
	} else if (x <= 5.6e+109) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6.4e+106:
		tmp = x
	elif x <= 5.6e+109:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.4e+106)
		tmp = x;
	elseif (x <= 5.6e+109)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6.4e+106)
		tmp = x;
	elseif (x <= 5.6e+109)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.4e+106], x, If[LessEqual[x, 5.6e+109], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.3999999999999996e106 or 5.6000000000000004e109 < x

   1. Initial program 94.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 37.0%

      \[\leadsto \color{blue}{x} \]

   if -6.3999999999999996e106 < x < 5.6000000000000004e109

   1. Initial program 95.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
   3. Step-by-step derivation

      1. negate-sub2 N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

         \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(t - 1\right)\right) \cdot \color{blue}{a} \]

      4. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot \left(t - 1\right)\right) \cdot \color{blue}{a} \]

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. negate-sub2 N/A

         \[\leadsto \left(1 - t\right) \cdot a \]

      7. lower--.f64 31.5

         \[\leadsto \left(1 - t\right) \cdot a \]

   4. Applied rewrites 31.5%

      \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

   5. Taylor expanded in t around 0

      \[\leadsto a \]
   6. Step-by-step derivation

   7. Applied rewrites 12.7%

      \[\leadsto a \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 15.6% accurate, 28.4× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, 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
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 95.0%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

2. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
3. Step-by-step derivation

4. Applied rewrites 15.6%

   \[\leadsto \color{blue}{x} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025110 
(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)))