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

Percentage Accurate: 95.5% → 97.8%

Time: 5.8s

Alternatives: 19

Speedup: 1.1×

• 35.9% 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: 95.5% 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: 97.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.5%

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

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

   4. lift--.f64 N/A

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

   5. sub-flip N/A

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

   6. +-commutative N/A

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

   7. associate--l+ N/A

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

   8. lift-*.f64 N/A

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

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

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

   10. lift--.f64 N/A

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

   11. sub-negate-rev N/A

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

   12. lower-fma.f64 N/A

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

   13. lower--.f64 N/A

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

   14. lower--.f64 N/A

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

   15. sub-flip N/A

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

   16. +-commutative N/A

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

3. Applied rewrites 97.8%

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

Alternative 2: 97.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.5%

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

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 97.4

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

   5. lift--.f64 N/A

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

   6. sub-negate-rev N/A

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

   7. lift-+.f64 N/A

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

   8. associate--r+ N/A

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

   9. sub-negate N/A

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

   10. lower--.f64 N/A

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

   11. lower--.f64 97.4

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

   12. lift--.f64 N/A

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

   13. lift-*.f64 N/A

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

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

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

   15. +-commutative N/A

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

   16. lift--.f64 N/A

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

   17. sub-negate-rev N/A

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

   18. lower-fma.f64 N/A

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

   19. lower--.f64 97.8

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

   20. lift--.f64 N/A

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

3. Applied rewrites 97.8%

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

Alternative 3: 94.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - y, z, x - t \cdot \left(a + -1 \cdot b\right)\right)\\ \mathbf{if}\;t \leq -3 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+25}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x - \mathsf{fma}\left(-1, a, b \cdot \left(2 - y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 y) z (- x (* t (+ a (* -1.0 b)))))))
   (if (<= t -3e-31)
     t_1
     (if (<= t 3e+25)
       (fma (- 1.0 y) z (- x (fma -1.0 a (* b (- 2.0 y)))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - y), z, (x - (t * (a + (-1.0 * b)))));
	double tmp;
	if (t <= -3e-31) {
		tmp = t_1;
	} else if (t <= 3e+25) {
		tmp = fma((1.0 - y), z, (x - fma(-1.0, a, (b * (2.0 - y)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - y), z, Float64(x - Float64(t * Float64(a + Float64(-1.0 * b)))))
	tmp = 0.0
	if (t <= -3e-31)
		tmp = t_1;
	elseif (t <= 3e+25)
		tmp = fma(Float64(1.0 - y), z, Float64(x - fma(-1.0, a, Float64(b * Float64(2.0 - y)))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z + N[(x - N[(t * N[(a + N[(-1.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3e-31], t$95$1, If[LessEqual[t, 3e+25], N[(N[(1.0 - y), $MachinePrecision] * z + N[(x - N[(-1.0 * a + N[(b * N[(2.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.99999999999999981e-31 or 3.00000000000000006e25 < t

   1. Initial program 95.5%

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

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

      4. lift--.f64 N/A

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

      5. sub-flip N/A

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

      6. +-commutative N/A

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

      7. associate--l+ N/A

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

      8. lift-*.f64 N/A

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

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

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower-fma.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 N/A

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

      15. sub-flip N/A

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

      16. +-commutative N/A

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 71.4

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

   6. Applied rewrites 71.4%

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

   if -2.99999999999999981e-31 < t < 3.00000000000000006e25

   1. Initial program 95.5%

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

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

      4. lift--.f64 N/A

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

      5. sub-flip N/A

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

      6. +-commutative N/A

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

      7. associate--l+ N/A

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

      8. lift-*.f64 N/A

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

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

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower-fma.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 N/A

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

      15. sub-flip N/A

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

      16. +-commutative N/A

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in t around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 69.2

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

   6. Applied rewrites 69.2%

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

Alternative 4: 93.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - y, z, x - t \cdot \left(a + -1 \cdot b\right)\right)\\ \mathbf{if}\;t \leq -3700000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+25}:\\ \;\;\;\;a + \left(x + \mathsf{fma}\left(b, y - 2, z \cdot \left(1 - y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 y) z (- x (* t (+ a (* -1.0 b)))))))
   (if (<= t -3700000.0)
     t_1
     (if (<= t 3e+25) (+ a (+ x (fma b (- y 2.0) (* z (- 1.0 y))))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - y), z, (x - (t * (a + (-1.0 * b)))));
	double tmp;
	if (t <= -3700000.0) {
		tmp = t_1;
	} else if (t <= 3e+25) {
		tmp = a + (x + fma(b, (y - 2.0), (z * (1.0 - y))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - y), z, Float64(x - Float64(t * Float64(a + Float64(-1.0 * b)))))
	tmp = 0.0
	if (t <= -3700000.0)
		tmp = t_1;
	elseif (t <= 3e+25)
		tmp = Float64(a + Float64(x + fma(b, Float64(y - 2.0), Float64(z * Float64(1.0 - y)))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z + N[(x - N[(t * N[(a + N[(-1.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3700000.0], t$95$1, If[LessEqual[t, 3e+25], N[(a + N[(x + N[(b * N[(y - 2.0), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.7e6 or 3.00000000000000006e25 < t

   1. Initial program 95.5%

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

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

      4. lift--.f64 N/A

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

      5. sub-flip N/A

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

      6. +-commutative N/A

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

      7. associate--l+ N/A

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

      8. lift-*.f64 N/A

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

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

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower-fma.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 N/A

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

      15. sub-flip N/A

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

      16. +-commutative N/A

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 71.4

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

   6. Applied rewrites 71.4%

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

   if -3.7e6 < t < 3.00000000000000006e25

   1. Initial program 95.5%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 77.5

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

   4. Applied rewrites 77.5%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-flip N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lift--.f64 N/A

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

      11. *-rgt-identity N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-rgt-identity N/A

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

      15. lower-+.f64 78.0

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

   6. Applied rewrites 78.0%

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

   7. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 69.4

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

   9. Applied rewrites 69.4%

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

Alternative 5: 88.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - \left(2 - y\right), b, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{if}\;y \leq -3.15 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-7}:\\ \;\;\;\;\left(x + z\right) - \mathsf{fma}\left(a, t - 1, b \cdot \left(2 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- t (- 2.0 y)) b (fma z (- 1.0 y) x))))
   (if (<= y -3.15e-9)
     t_1
     (if (<= y 1.8e-7) (- (+ x z) (fma a (- t 1.0) (* b (- 2.0 t)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((t - (2.0 - y)), b, fma(z, (1.0 - y), x));
	double tmp;
	if (y <= -3.15e-9) {
		tmp = t_1;
	} else if (y <= 1.8e-7) {
		tmp = (x + z) - fma(a, (t - 1.0), (b * (2.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(t - Float64(2.0 - y)), b, fma(z, Float64(1.0 - y), x))
	tmp = 0.0
	if (y <= -3.15e-9)
		tmp = t_1;
	elseif (y <= 1.8e-7)
		tmp = Float64(Float64(x + z) - fma(a, Float64(t - 1.0), Float64(b * Float64(2.0 - t))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - N[(2.0 - y), $MachinePrecision]), $MachinePrecision] * b + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.15e-9], t$95$1, If[LessEqual[y, 1.8e-7], N[(N[(x + z), $MachinePrecision] - N[(a * N[(t - 1.0), $MachinePrecision] + N[(b * N[(2.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.1500000000000001e-9 or 1.79999999999999997e-7 < y

   1. Initial program 95.5%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 73.2

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

   4. Applied rewrites 73.2%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate--l+ N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lower-fma.f64 74.2

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

      12. lift--.f64 N/A

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

      13. lift-+.f64 N/A

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

      14. associate--l+ N/A

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

      15. add-flip-rev N/A

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

      16. sub-negate-rev N/A

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

      17. lift--.f64 N/A

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

      18. lower--.f64 74.2

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

      19. lift--.f64 N/A

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

      20. lift-*.f64 N/A

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

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

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

      22. lift--.f64 N/A

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

      23. sub-negate-rev N/A

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

      24. lift--.f64 N/A

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

      25. +-commutative N/A

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

   6. Applied rewrites 74.2%

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

   if -3.1500000000000001e-9 < y < 1.79999999999999997e-7

   1. Initial program 95.5%

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

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

      4. lift--.f64 N/A

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

      5. sub-flip N/A

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

      6. +-commutative N/A

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

      7. associate--l+ N/A

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

      8. lift-*.f64 N/A

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

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

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower-fma.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 N/A

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

      15. sub-flip N/A

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

      16. +-commutative N/A

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 70.9

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

   6. Applied rewrites 70.9%

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

Alternative 6: 86.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{if}\;a \leq -2500:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, t\_1\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+116}:\\ \;\;\;\;\mathsf{fma}\left(t - \left(2 - y\right), b, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(a, 1 - t, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma z (- 1.0 y) x)))
   (if (<= a -2500.0)
     (fma (- 1.0 t) a t_1)
     (if (<= a 3.4e+116)
       (fma (- t (- 2.0 y)) b t_1)
       (fma (- 1.0 y) z (fma a (- 1.0 t) x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(z, (1.0 - y), x);
	double tmp;
	if (a <= -2500.0) {
		tmp = fma((1.0 - t), a, t_1);
	} else if (a <= 3.4e+116) {
		tmp = fma((t - (2.0 - y)), b, t_1);
	} else {
		tmp = fma((1.0 - y), z, fma(a, (1.0 - t), x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(z, Float64(1.0 - y), x)
	tmp = 0.0
	if (a <= -2500.0)
		tmp = fma(Float64(1.0 - t), a, t_1);
	elseif (a <= 3.4e+116)
		tmp = fma(Float64(t - Float64(2.0 - y)), b, t_1);
	else
		tmp = fma(Float64(1.0 - y), z, fma(a, Float64(1.0 - t), x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -2500.0], N[(N[(1.0 - t), $MachinePrecision] * a + t$95$1), $MachinePrecision], If[LessEqual[a, 3.4e+116], N[(N[(t - N[(2.0 - y), $MachinePrecision]), $MachinePrecision] * b + t$95$1), $MachinePrecision], N[(N[(1.0 - y), $MachinePrecision] * z + N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2500

   1. Initial program 95.5%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 28.6

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

   4. Applied rewrites 28.6%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 11.1%

      \[\leadsto a \]

   8. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 67.2

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

   10. Applied rewrites 67.2%

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

       1. lift--.f64 N/A

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

       2. lift--.f64 N/A

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

       3. lift-fma.f64 N/A

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

       4. +-commutative N/A

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

       5. lift-*.f64 N/A

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

       6. *-commutative N/A

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

       7. lift--.f64 N/A

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

       8. *-commutative N/A

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

       9. associate--l- N/A

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

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

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

       11. +-commutative N/A

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

       12. sub-negate-rev N/A

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

       13. remove-double-neg N/A

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

       14. mul-1-neg N/A

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

       15. lower-fma.f64 N/A

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

       16. lower--.f64 N/A

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

       17. mul-1-neg N/A

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

       18. remove-double-neg N/A

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

       19. sub-negate-rev N/A

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

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

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

       21. +-commutative N/A

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

   12. Applied rewrites 67.2%

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

   if -2500 < a < 3.40000000000000023e116

   1. Initial program 95.5%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 73.2

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

   4. Applied rewrites 73.2%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate--l+ N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lower-fma.f64 74.2

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

      12. lift--.f64 N/A

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

      13. lift-+.f64 N/A

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

      14. associate--l+ N/A

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

      15. add-flip-rev N/A

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

      16. sub-negate-rev N/A

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

      17. lift--.f64 N/A

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

      18. lower--.f64 74.2

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

      19. lift--.f64 N/A

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

      20. lift-*.f64 N/A

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

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

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

      22. lift--.f64 N/A

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

      23. sub-negate-rev N/A

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

      24. lift--.f64 N/A

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

      25. +-commutative N/A

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

   6. Applied rewrites 74.2%

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

   if 3.40000000000000023e116 < a

   1. Initial program 95.5%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 28.6

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

   4. Applied rewrites 28.6%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 11.1%

      \[\leadsto a \]

   8. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 67.2

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

   10. Applied rewrites 67.2%

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

       1. lift--.f64 N/A

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

       2. lift--.f64 N/A

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

       3. lift-fma.f64 N/A

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

       4. associate--r+ N/A

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

       5. lift-*.f64 N/A

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

       6. *-commutative N/A

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

       7. lift--.f64 N/A

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

       8. sub-negate-rev N/A

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

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

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

       10. +-commutative N/A

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

       11. *-commutative N/A

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

       12. sub-negate-rev N/A

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

       13. lift--.f64 N/A

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

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

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

       15. lift-*.f64 N/A

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

       16. sub-negate-rev N/A

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

       17. lift-*.f64 N/A

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

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

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

       19. *-rgt-identity N/A

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

       20. lift--.f64 N/A

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

       21. sub-negate-rev N/A

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

       22. *-commutative N/A

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

   12. Applied rewrites 67.1%

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

Alternative 7: 84.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - \left(2 - t\right), b, x - z \cdot -1\right)\\ \mathbf{if}\;b \leq -4.8 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+98}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(a, 1 - t, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- y (- 2.0 t)) b (- x (* z -1.0)))))
   (if (<= b -4.8e+129)
     t_1
     (if (<= b 5.4e+98) (fma (- 1.0 y) z (fma a (- 1.0 t) x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((y - (2.0 - t)), b, (x - (z * -1.0)));
	double tmp;
	if (b <= -4.8e+129) {
		tmp = t_1;
	} else if (b <= 5.4e+98) {
		tmp = fma((1.0 - y), z, fma(a, (1.0 - t), x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(y - Float64(2.0 - t)), b, Float64(x - Float64(z * -1.0)))
	tmp = 0.0
	if (b <= -4.8e+129)
		tmp = t_1;
	elseif (b <= 5.4e+98)
		tmp = fma(Float64(1.0 - y), z, fma(a, Float64(1.0 - t), x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y - N[(2.0 - t), $MachinePrecision]), $MachinePrecision] * b + N[(x - N[(z * -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.8e+129], t$95$1, If[LessEqual[b, 5.4e+98], N[(N[(1.0 - y), $MachinePrecision] * z + N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -4.7999999999999997e129 or 5.4e98 < b

   1. Initial program 95.5%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 73.2

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

   4. Applied rewrites 73.2%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 60.1%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. associate--l+ N/A

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

      13. +-commutative N/A

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

      14. associate-+l- N/A

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

      15. lower--.f64 N/A

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

      16. lower--.f64 N/A

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

      17. add-flip N/A

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

      18. lower--.f64 N/A

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

   9. Applied rewrites 60.1%

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

   if -4.7999999999999997e129 < b < 5.4e98

   1. Initial program 95.5%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 28.6

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

   4. Applied rewrites 28.6%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 11.1%

      \[\leadsto a \]

   8. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 67.2

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

   10. Applied rewrites 67.2%

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

       1. lift--.f64 N/A

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

       2. lift--.f64 N/A

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

       3. lift-fma.f64 N/A

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

       4. associate--r+ N/A

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

       5. lift-*.f64 N/A

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

       6. *-commutative N/A

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

       7. lift--.f64 N/A

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

       8. sub-negate-rev N/A

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

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

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

       10. +-commutative N/A

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

       11. *-commutative N/A

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

       12. sub-negate-rev N/A

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

       13. lift--.f64 N/A

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

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

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

       15. lift-*.f64 N/A

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

       16. sub-negate-rev N/A

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

       17. lift-*.f64 N/A

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

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

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

       19. *-rgt-identity N/A

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

       20. lift--.f64 N/A

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

       21. sub-negate-rev N/A

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

       22. *-commutative N/A

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

   12. Applied rewrites 67.1%

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

Alternative 8: 82.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - \left(2 - y\right)\right) \cdot b\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+101}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(a, 1 - t, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t (- 2.0 y)) b)))
   (if (<= b -1.25e+154)
     t_1
     (if (<= b 3.8e+101) (fma (- 1.0 y) z (fma a (- 1.0 t) x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - (2.0 - y)) * b;
	double tmp;
	if (b <= -1.25e+154) {
		tmp = t_1;
	} else if (b <= 3.8e+101) {
		tmp = fma((1.0 - y), z, fma(a, (1.0 - t), x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - Float64(2.0 - y)) * b)
	tmp = 0.0
	if (b <= -1.25e+154)
		tmp = t_1;
	elseif (b <= 3.8e+101)
		tmp = fma(Float64(1.0 - y), z, fma(a, Float64(1.0 - t), x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - N[(2.0 - y), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.25e+154], t$95$1, If[LessEqual[b, 3.8e+101], N[(N[(1.0 - y), $MachinePrecision] * z + N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.25000000000000001e154 or 3.7999999999999998e101 < b

   1. Initial program 95.5%

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

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

      4. lift--.f64 N/A

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

      5. sub-flip N/A

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

      6. +-commutative N/A

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

      7. associate--l+ N/A

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

      8. lift-*.f64 N/A

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

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

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower-fma.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 N/A

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

      15. sub-flip N/A

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

      16. +-commutative N/A

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in b around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 37.5

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

   6. Applied rewrites 37.5%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. lift--.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. sub-negate-rev N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. associate--l- N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 N/A

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

      15. lower--.f64 37.5

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

   8. Applied rewrites 37.5%

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

   if -1.25000000000000001e154 < b < 3.7999999999999998e101

   1. Initial program 95.5%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 28.6

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

   4. Applied rewrites 28.6%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 11.1%

      \[\leadsto a \]

   8. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 67.2

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

   10. Applied rewrites 67.2%

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

       1. lift--.f64 N/A

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

       2. lift--.f64 N/A

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

       3. lift-fma.f64 N/A

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

       4. associate--r+ N/A

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

       5. lift-*.f64 N/A

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

       6. *-commutative N/A

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

       7. lift--.f64 N/A

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

       8. sub-negate-rev N/A

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

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

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

       10. +-commutative N/A

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

       11. *-commutative N/A

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

       12. sub-negate-rev N/A

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

       13. lift--.f64 N/A

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

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

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

       15. lift-*.f64 N/A

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

       16. sub-negate-rev N/A

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

       17. lift-*.f64 N/A

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

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

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

       19. *-rgt-identity N/A

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

       20. lift--.f64 N/A

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

       21. sub-negate-rev N/A

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

       22. *-commutative N/A

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

   12. Applied rewrites 67.1%

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

Alternative 9: 82.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - \left(2 - y\right)\right) \cdot b\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+101}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t (- 2.0 y)) b)))
   (if (<= b -1.25e+154)
     t_1
     (if (<= b 3.8e+101) (fma (- 1.0 t) a (fma z (- 1.0 y) x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - (2.0 - y)) * b;
	double tmp;
	if (b <= -1.25e+154) {
		tmp = t_1;
	} else if (b <= 3.8e+101) {
		tmp = fma((1.0 - t), a, fma(z, (1.0 - y), x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - Float64(2.0 - y)) * b)
	tmp = 0.0
	if (b <= -1.25e+154)
		tmp = t_1;
	elseif (b <= 3.8e+101)
		tmp = fma(Float64(1.0 - t), a, fma(z, Float64(1.0 - y), x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - N[(2.0 - y), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.25e+154], t$95$1, If[LessEqual[b, 3.8e+101], N[(N[(1.0 - t), $MachinePrecision] * a + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.25000000000000001e154 or 3.7999999999999998e101 < b

   1. Initial program 95.5%

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

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

      4. lift--.f64 N/A

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

      5. sub-flip N/A

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

      6. +-commutative N/A

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

      7. associate--l+ N/A

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

      8. lift-*.f64 N/A

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

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

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower-fma.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 N/A

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

      15. sub-flip N/A

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

      16. +-commutative N/A

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in b around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 37.5

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

   6. Applied rewrites 37.5%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. lift--.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. sub-negate-rev N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. associate--l- N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 N/A

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

      15. lower--.f64 37.5

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

   8. Applied rewrites 37.5%

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

   if -1.25000000000000001e154 < b < 3.7999999999999998e101

   1. Initial program 95.5%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 28.6

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

   4. Applied rewrites 28.6%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 11.1%

      \[\leadsto a \]

   8. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 67.2

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

   10. Applied rewrites 67.2%

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

       1. lift--.f64 N/A

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

       2. lift--.f64 N/A

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

       3. lift-fma.f64 N/A

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

       4. +-commutative N/A

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

       5. lift-*.f64 N/A

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

       6. *-commutative N/A

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

       7. lift--.f64 N/A

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

       8. *-commutative N/A

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

       9. associate--l- N/A

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

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

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

       11. +-commutative N/A

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

       12. sub-negate-rev N/A

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

       13. remove-double-neg N/A

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

       14. mul-1-neg N/A

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

       15. lower-fma.f64 N/A

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

       16. lower--.f64 N/A

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

       17. mul-1-neg N/A

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

       18. remove-double-neg N/A

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

       19. sub-negate-rev N/A

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

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

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

       21. +-commutative N/A

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

   12. Applied rewrites 67.2%

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

Alternative 10: 67.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3.55 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+31}:\\ \;\;\;\;x - \mathsf{fma}\left(-1, a, z \cdot \left(y - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -3.55e+75)
     t_1
     (if (<= t 2.3e+31) (- x (fma -1.0 a (* z (- y 1.0)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -3.55e+75) {
		tmp = t_1;
	} else if (t <= 2.3e+31) {
		tmp = x - fma(-1.0, a, (z * (y - 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -3.55e+75)
		tmp = t_1;
	elseif (t <= 2.3e+31)
		tmp = Float64(x - fma(-1.0, a, Float64(z * Float64(y - 1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.55e+75], t$95$1, If[LessEqual[t, 2.3e+31], N[(x - N[(-1.0 * a + N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.54999999999999991e75 or 2.3e31 < t

   1. Initial program 95.5%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 33.5

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

   4. Applied rewrites 33.5%

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

   if -3.54999999999999991e75 < t < 2.3e31

   1. Initial program 95.5%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 28.6

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

   4. Applied rewrites 28.6%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 11.1%

      \[\leadsto a \]

   8. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 67.2

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

   10. Applied rewrites 67.2%

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

   11. Taylor expanded in t around 0

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

       1. lower-fma.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 50.4

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

   13. Applied rewrites 50.4%

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

Alternative 11: 58.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+31}:\\ \;\;\;\;x - z \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -5.6e+67) t_1 (if (<= t 2.3e+31) (- x (* z (- y 1.0))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -5.6e+67) {
		tmp = t_1;
	} else if (t <= 2.3e+31) {
		tmp = x - (z * (y - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-5.6d+67)) then
        tmp = t_1
    else if (t <= 2.3d+31) then
        tmp = x - (z * (y - 1.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -5.6e+67) {
		tmp = t_1;
	} else if (t <= 2.3e+31) {
		tmp = x - (z * (y - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -5.6e+67:
		tmp = t_1
	elif t <= 2.3e+31:
		tmp = x - (z * (y - 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -5.6e+67)
		tmp = t_1;
	elseif (t <= 2.3e+31)
		tmp = Float64(x - Float64(z * Float64(y - 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -5.6e+67)
		tmp = t_1;
	elseif (t <= 2.3e+31)
		tmp = x - (z * (y - 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e+67], t$95$1, If[LessEqual[t, 2.3e+31], N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.5999999999999995e67 or 2.3e31 < t

   1. Initial program 95.5%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 33.5

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

   4. Applied rewrites 33.5%

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

   if -5.5999999999999995e67 < t < 2.3e31

   1. Initial program 95.5%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 73.2

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

   4. Applied rewrites 73.2%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 60.1%

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

   8. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 41.3

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

   10. Applied rewrites 41.3%

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

Alternative 12: 51.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+16}:\\ \;\;\;\;x - a \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -7.5e-28) t_1 (if (<= y 2.9e+16) (- x (* a t)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -7.5e-28) {
		tmp = t_1;
	} else if (y <= 2.9e+16) {
		tmp = x - (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-7.5d-28)) then
        tmp = t_1
    else if (y <= 2.9d+16) then
        tmp = x - (a * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -7.5e-28) {
		tmp = t_1;
	} else if (y <= 2.9e+16) {
		tmp = x - (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -7.5e-28:
		tmp = t_1
	elif y <= 2.9e+16:
		tmp = x - (a * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -7.5e-28)
		tmp = t_1;
	elseif (y <= 2.9e+16)
		tmp = Float64(x - Float64(a * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -7.5e-28)
		tmp = t_1;
	elseif (y <= 2.9e+16)
		tmp = x - (a * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.5e-28], t$95$1, If[LessEqual[y, 2.9e+16], N[(x - N[(a * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5000000000000003e-28 or 2.9e16 < y

   1. Initial program 95.5%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 32.0

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

   4. Applied rewrites 32.0%

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

   if -7.5000000000000003e-28 < y < 2.9e16

   1. Initial program 95.5%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 28.6

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

   4. Applied rewrites 28.6%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 11.1%

      \[\leadsto a \]

   8. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 67.2

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

   10. Applied rewrites 67.2%

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

   11. Taylor expanded in t around inf

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

       1. lower-*.f64 32.8

          \[\leadsto x - a \cdot t \]

   13. Applied rewrites 32.8%

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

Alternative 13: 50.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -3.5e+61) t_1 (if (<= t 2.3e+31) (* y (- b z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -3.5e+61) {
		tmp = t_1;
	} else if (t <= 2.3e+31) {
		tmp = y * (b - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-3.5d+61)) then
        tmp = t_1
    else if (t <= 2.3d+31) then
        tmp = y * (b - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -3.5e+61) {
		tmp = t_1;
	} else if (t <= 2.3e+31) {
		tmp = y * (b - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -3.5e+61:
		tmp = t_1
	elif t <= 2.3e+31:
		tmp = y * (b - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -3.5e+61)
		tmp = t_1;
	elseif (t <= 2.3e+31)
		tmp = Float64(y * Float64(b - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -3.5e+61)
		tmp = t_1;
	elseif (t <= 2.3e+31)
		tmp = y * (b - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e+61], t$95$1, If[LessEqual[t, 2.3e+31], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.50000000000000018e61 or 2.3e31 < t

   1. Initial program 95.5%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 33.5

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

   4. Applied rewrites 33.5%

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

   if -3.50000000000000018e61 < t < 2.3e31

   1. Initial program 95.5%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 32.0

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

   4. Applied rewrites 32.0%

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

Alternative 14: 42.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3700000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+30}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -3700000.0) t_1 (if (<= t 2.8e+30) (* y b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -3700000.0) {
		tmp = t_1;
	} else if (t <= 2.8e+30) {
		tmp = y * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-3700000.0d0)) then
        tmp = t_1
    else if (t <= 2.8d+30) then
        tmp = y * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -3700000.0) {
		tmp = t_1;
	} else if (t <= 2.8e+30) {
		tmp = y * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -3700000.0:
		tmp = t_1
	elif t <= 2.8e+30:
		tmp = y * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -3700000.0)
		tmp = t_1;
	elseif (t <= 2.8e+30)
		tmp = Float64(y * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -3700000.0)
		tmp = t_1;
	elseif (t <= 2.8e+30)
		tmp = y * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3700000.0], t$95$1, If[LessEqual[t, 2.8e+30], N[(y * b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.7e6 or 2.79999999999999983e30 < t

   1. Initial program 95.5%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 33.5

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

   4. Applied rewrites 33.5%

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

   if -3.7e6 < t < 2.79999999999999983e30

   1. Initial program 95.5%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 32.0

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

   4. Applied rewrites 32.0%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 17.1%

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

Alternative 15: 33.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+188}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 8.1 \cdot 10^{+133}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.1e+188) (* y b) (if (<= b 8.1e+133) (* a (- 1.0 t)) (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.1e+188) {
		tmp = y * b;
	} else if (b <= 8.1e+133) {
		tmp = a * (1.0 - t);
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.1d+188)) then
        tmp = y * b
    else if (b <= 8.1d+133) then
        tmp = a * (1.0d0 - t)
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.1e+188) {
		tmp = y * b;
	} else if (b <= 8.1e+133) {
		tmp = a * (1.0 - t);
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.1e+188:
		tmp = y * b
	elif b <= 8.1e+133:
		tmp = a * (1.0 - t)
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.1e+188)
		tmp = Float64(y * b);
	elseif (b <= 8.1e+133)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.1e+188)
		tmp = y * b;
	elseif (b <= 8.1e+133)
		tmp = a * (1.0 - t);
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.1e+188], N[(y * b), $MachinePrecision], If[LessEqual[b, 8.1e+133], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], N[(y * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.09999999999999999e188 or 8.0999999999999996e133 < b

   1. Initial program 95.5%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 32.0

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

   4. Applied rewrites 32.0%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 17.1%

      \[\leadsto y \cdot b \]

   if -1.09999999999999999e188 < b < 8.0999999999999996e133

   1. Initial program 95.5%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 28.6

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

   4. Applied rewrites 28.6%

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

Alternative 16: 27.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+70}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 3.45 \cdot 10^{+106}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2e+70) (* b t) (if (<= t 3.45e+106) (* y b) (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2e+70) {
		tmp = b * t;
	} else if (t <= 3.45e+106) {
		tmp = y * b;
	} 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 <= (-2d+70)) then
        tmp = b * t
    else if (t <= 3.45d+106) then
        tmp = y * b
    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 <= -2e+70) {
		tmp = b * t;
	} else if (t <= 3.45e+106) {
		tmp = y * b;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2e+70:
		tmp = b * t
	elif t <= 3.45e+106:
		tmp = y * b
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2e+70)
		tmp = Float64(b * t);
	elseif (t <= 3.45e+106)
		tmp = Float64(y * b);
	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 <= -2e+70)
		tmp = b * t;
	elseif (t <= 3.45e+106)
		tmp = y * b;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2e+70], N[(b * t), $MachinePrecision], If[LessEqual[t, 3.45e+106], N[(y * b), $MachinePrecision], N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.00000000000000015e70 or 3.4499999999999999e106 < t

   1. Initial program 95.5%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 73.2

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

   4. Applied rewrites 73.2%

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

   5. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{t} \]
   6. Step-by-step derivation

      1. lower-*.f64 17.9

         \[\leadsto b \cdot t \]

   7. Applied rewrites 17.9%

      \[\leadsto b \cdot \color{blue}{t} \]

   if -2.00000000000000015e70 < t < 3.4499999999999999e106

   1. Initial program 95.5%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 32.0

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

   4. Applied rewrites 32.0%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 17.1%

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

Alternative 17: 22.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+24}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+130}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.5e+24) (* b t) (if (<= t 3.5e+130) z (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.5e+24) {
		tmp = b * t;
	} else if (t <= 3.5e+130) {
		tmp = z;
	} 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 <= (-7.5d+24)) then
        tmp = b * t
    else if (t <= 3.5d+130) then
        tmp = z
    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 <= -7.5e+24) {
		tmp = b * t;
	} else if (t <= 3.5e+130) {
		tmp = z;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.5e+24:
		tmp = b * t
	elif t <= 3.5e+130:
		tmp = z
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.5e+24)
		tmp = Float64(b * t);
	elseif (t <= 3.5e+130)
		tmp = z;
	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 <= -7.5e+24)
		tmp = b * t;
	elseif (t <= 3.5e+130)
		tmp = z;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.5e+24], N[(b * t), $MachinePrecision], If[LessEqual[t, 3.5e+130], z, N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.50000000000000014e24 or 3.5000000000000001e130 < t

   1. Initial program 95.5%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 73.2

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

   4. Applied rewrites 73.2%

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

   5. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{t} \]
   6. Step-by-step derivation

      1. lower-*.f64 17.9

         \[\leadsto b \cdot t \]

   7. Applied rewrites 17.9%

      \[\leadsto b \cdot \color{blue}{t} \]

   if -7.50000000000000014e24 < t < 3.5000000000000001e130

   1. Initial program 95.5%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 28.1

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

   4. Applied rewrites 28.1%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 11.3%

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

Alternative 18: 17.3% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+85}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+111}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -5.8e+85) a (if (<= a 6.5e+111) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5.8e+85) {
		tmp = a;
	} else if (a <= 6.5e+111) {
		tmp = z;
	} else {
		tmp = a;
	}
	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 (a <= (-5.8d+85)) then
        tmp = a
    else if (a <= 6.5d+111) then
        tmp = z
    else
        tmp = a
    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 (a <= -5.8e+85) {
		tmp = a;
	} else if (a <= 6.5e+111) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -5.8e+85:
		tmp = a
	elif a <= 6.5e+111:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -5.8e+85)
		tmp = a;
	elseif (a <= 6.5e+111)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -5.8e+85)
		tmp = a;
	elseif (a <= 6.5e+111)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -5.8e+85], a, If[LessEqual[a, 6.5e+111], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -5.79999999999999995e85 or 6.5000000000000002e111 < a

   1. Initial program 95.5%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 28.6

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

   4. Applied rewrites 28.6%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 11.1%

      \[\leadsto a \]

   if -5.79999999999999995e85 < a < 6.5000000000000002e111

   1. Initial program 95.5%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 28.1

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

   4. Applied rewrites 28.1%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 11.3%

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

Alternative 19: 11.1% accurate, 28.4× speedup

Math

\[\begin{array}{l} \\ a \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 a)

C

double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = a
end function

Java

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

Python

def code(x, y, z, t, a, b):
	return a

Julia

function code(x, y, z, t, a, b)
	return a
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := a

Derivation

1. Initial program 95.5%

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

2. Taylor expanded in a around inf

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

   1. lower-*.f64 N/A

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

   2. lower--.f64 28.6

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

4. Applied rewrites 28.6%

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

5. Taylor expanded in t around 0

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

7. Applied rewrites 11.1%

   \[\leadsto a \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025154 
(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)))