Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.9% → 87.8%

Time: 5.6s

Alternatives: 12

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + ((y - z) * ((t - x) / (a - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + ((y - z) * ((t - x) / (a - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-218}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{-142}:\\ \;\;\;\;\left(-\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\right) + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -5e-218)
     t_1
     (if (<= t_1 1e-142) (+ (- (/ (* (- t x) (- y a)) z)) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -5e-218) {
		tmp = t_1;
	} else if (t_1 <= 1e-142) {
		tmp = -(((t - x) * (y - a)) / z) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_1 <= (-5d-218)) then
        tmp = t_1
    else if (t_1 <= 1d-142) then
        tmp = -(((t - x) * (y - a)) / z) + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -5e-218) {
		tmp = t_1;
	} else if (t_1 <= 1e-142) {
		tmp = -(((t - x) * (y - a)) / z) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -5e-218:
		tmp = t_1
	elif t_1 <= 1e-142:
		tmp = -(((t - x) * (y - a)) / z) + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -5e-218)
		tmp = t_1;
	elseif (t_1 <= 1e-142)
		tmp = Float64(Float64(-Float64(Float64(Float64(t - x) * Float64(y - a)) / z)) + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -5e-218)
		tmp = t_1;
	elseif (t_1 <= 1e-142)
		tmp = -(((t - x) * (y - a)) / z) + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-218], t$95$1, If[LessEqual[t$95$1, 1e-142], N[((-N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]) + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.00000000000000041e-218 or 1e-142 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.0%

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

   if -5.00000000000000041e-218 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1e-142

   1. Initial program 23.3%

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

   2. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. sub-div N/A

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

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

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

   4. Applied rewrites 67.9%

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

Alternative 2: 87.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := \mathsf{fma}\left(t\_1, y - z, x\right)\\ t_3 := x + \left(y - z\right) \cdot t\_1\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{-218}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 10^{-142}:\\ \;\;\;\;\left(-\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\right) + t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z)))
        (t_2 (fma t_1 (- y z) x))
        (t_3 (+ x (* (- y z) t_1))))
   (if (<= t_3 -5e-218)
     t_2
     (if (<= t_3 1e-142) (+ (- (/ (* (- t x) (- y a)) z)) t) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = fma(t_1, (y - z), x);
	double t_3 = x + ((y - z) * t_1);
	double tmp;
	if (t_3 <= -5e-218) {
		tmp = t_2;
	} else if (t_3 <= 1e-142) {
		tmp = -(((t - x) * (y - a)) / z) + t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = fma(t_1, Float64(y - z), x)
	t_3 = Float64(x + Float64(Float64(y - z) * t_1))
	tmp = 0.0
	if (t_3 <= -5e-218)
		tmp = t_2;
	elseif (t_3 <= 1e-142)
		tmp = Float64(Float64(-Float64(Float64(Float64(t - x) * Float64(y - a)) / z)) + t);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e-218], t$95$2, If[LessEqual[t$95$3, 1e-142], N[((-N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]) + t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.00000000000000041e-218 or 1e-142 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 92.0

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

   3. Applied rewrites 92.0%

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

   if -5.00000000000000041e-218 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1e-142

   1. Initial program 23.3%

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

   2. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. sub-div N/A

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

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

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

   4. Applied rewrites 67.9%

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

Alternative 3: 72.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \mathbf{if}\;a \leq -31000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+73}:\\ \;\;\;\;\left(-\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\right) + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- t x) (/ (- y z) a) x)))
   (if (<= a -31000000000.0)
     t_1
     (if (<= a 5e+73) (+ (- (/ (* (- t x) (- y a)) z)) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t - x), ((y - z) / a), x);
	double tmp;
	if (a <= -31000000000.0) {
		tmp = t_1;
	} else if (a <= 5e+73) {
		tmp = -(((t - x) * (y - a)) / z) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t - x), Float64(Float64(y - z) / a), x)
	tmp = 0.0
	if (a <= -31000000000.0)
		tmp = t_1;
	elseif (a <= 5e+73)
		tmp = Float64(Float64(-Float64(Float64(Float64(t - x) * Float64(y - a)) / z)) + t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -31000000000.0], t$95$1, If[LessEqual[a, 5e+73], N[((-N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]) + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.1e10 or 4.99999999999999976e73 < a

   1. Initial program 88.1%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 78.3

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

   4. Applied rewrites 78.3%

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

   if -3.1e10 < a < 4.99999999999999976e73

   1. Initial program 73.6%

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

   2. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r/ N/A

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

      4. sub-div N/A

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

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

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

   4. Applied rewrites 68.9%

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

Alternative 4: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t}{a - z}, y - z, x\right)\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+24}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-50}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ t (- a z)) (- y z) x)) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= z -2.6e+24)
     t_2
     (if (<= z -1.65e-158)
       t_1
       (if (<= z 3.6e-50)
         (fma (- t x) (/ (- y z) a) x)
         (if (<= z 2.5e+142) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t / (a - z)), (y - z), x);
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.6e+24) {
		tmp = t_2;
	} else if (z <= -1.65e-158) {
		tmp = t_1;
	} else if (z <= 3.6e-50) {
		tmp = fma((t - x), ((y - z) / a), x);
	} else if (z <= 2.5e+142) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t / Float64(a - z)), Float64(y - z), x)
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -2.6e+24)
		tmp = t_2;
	elseif (z <= -1.65e-158)
		tmp = t_1;
	elseif (z <= 3.6e-50)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / a), x);
	elseif (z <= 2.5e+142)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+24], t$95$2, If[LessEqual[z, -1.65e-158], t$95$1, If[LessEqual[z, 3.6e-50], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 2.5e+142], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5999999999999998e24 or 2.5000000000000001e142 < z

   1. Initial program 63.2%

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

   2. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 59.4

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

   4. Applied rewrites 59.4%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 63.5

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

   7. Applied rewrites 63.5%

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

   if -2.5999999999999998e24 < z < -1.6500000000000001e-158 or 3.59999999999999979e-50 < z < 2.5000000000000001e142

   1. Initial program 87.3%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 87.4

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

   3. Applied rewrites 87.4%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 69.0%

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

   if -1.6500000000000001e-158 < z < 3.59999999999999979e-50

   1. Initial program 91.5%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 84.3

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

   4. Applied rewrites 84.3%

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

Alternative 5: 72.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -8200:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+93}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -8200.0)
     t_1
     (if (<= z 1.5e+93) (+ x (* y (/ (- t x) (- a z)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -8200.0) {
		tmp = t_1;
	} else if (z <= 1.5e+93) {
		tmp = x + (y * ((t - x) / (a - 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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-8200.0d0)) then
        tmp = t_1
    else if (z <= 1.5d+93) then
        tmp = x + (y * ((t - x) / (a - 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 t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -8200.0) {
		tmp = t_1;
	} else if (z <= 1.5e+93) {
		tmp = x + (y * ((t - x) / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -8200.0:
		tmp = t_1
	elif z <= 1.5e+93:
		tmp = x + (y * ((t - x) / (a - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -8200.0)
		tmp = t_1;
	elseif (z <= 1.5e+93)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / Float64(a - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -8200.0)
		tmp = t_1;
	elseif (z <= 1.5e+93)
		tmp = x + (y * ((t - x) / (a - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8200.0], t$95$1, If[LessEqual[z, 1.5e+93], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8200 or 1.49999999999999989e93 < z

   1. Initial program 65.3%

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

   2. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 61.1

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

   4. Applied rewrites 61.1%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 62.5

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

   7. Applied rewrites 62.5%

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

   if -8200 < z < 1.49999999999999989e93

   1. Initial program 90.7%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 80.6%

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

Alternative 6: 69.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -185000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+89}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -185000000000.0)
     t_1
     (if (<= z 1.95e+89) (fma (- t x) (/ (- y z) a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -185000000000.0) {
		tmp = t_1;
	} else if (z <= 1.95e+89) {
		tmp = fma((t - x), ((y - z) / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -185000000000.0)
		tmp = t_1;
	elseif (z <= 1.95e+89)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -185000000000.0], t$95$1, If[LessEqual[z, 1.95e+89], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.85e11 or 1.95000000000000005e89 < z

   1. Initial program 65.1%

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

   2. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 61.0

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

   4. Applied rewrites 61.0%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 62.8

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

   7. Applied rewrites 62.8%

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

   if -1.85e11 < z < 1.95000000000000005e89

   1. Initial program 90.6%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 74.5

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

   4. Applied rewrites 74.5%

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

Alternative 7: 67.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -2 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.0035:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -2e-32) t_1 (if (<= z 0.0035) (fma (- t x) (/ y a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2e-32) {
		tmp = t_1;
	} else if (z <= 0.0035) {
		tmp = fma((t - x), (y / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -2e-32)
		tmp = t_1;
	elseif (z <= 0.0035)
		tmp = fma(Float64(t - x), Float64(y / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e-32], t$95$1, If[LessEqual[z, 0.0035], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000011e-32 or 0.00350000000000000007 < z

   1. Initial program 69.6%

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

   2. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 64.6

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

   4. Applied rewrites 64.6%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. sub-div N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 60.1

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

   7. Applied rewrites 60.1%

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

   if -2.00000000000000011e-32 < z < 0.00350000000000000007

   1. Initial program 91.6%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 79.8

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 76.2%

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

Alternative 8: 60.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+39}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1e+39) t (if (<= z 2.6e+99) (fma (- t x) (/ y a) x) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e+39) {
		tmp = t;
	} else if (z <= 2.6e+99) {
		tmp = fma((t - x), (y / a), x);
	} else {
		tmp = t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1e+39)
		tmp = t;
	elseif (z <= 2.6e+99)
		tmp = fma(Float64(t - x), Float64(y / a), x);
	else
		tmp = t;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1e+39], t, If[LessEqual[z, 2.6e+99], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999994e38 or 2.6e99 < z

   1. Initial program 64.0%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 48.8%

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

   if -9.9999999999999994e38 < z < 2.6e99

   1. Initial program 90.1%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 73.2

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

   4. Applied rewrites 73.2%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 68.4%

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

Alternative 9: 59.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+39}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1e+39) t (if (<= z 2.6e+99) (fma y (/ (- t x) a) x) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e+39) {
		tmp = t;
	} else if (z <= 2.6e+99) {
		tmp = fma(y, ((t - x) / a), x);
	} else {
		tmp = t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1e+39)
		tmp = t;
	elseif (z <= 2.6e+99)
		tmp = fma(y, Float64(Float64(t - x) / a), x);
	else
		tmp = t;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1e+39], t, If[LessEqual[z, 2.6e+99], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999994e38 or 2.6e99 < z

   1. Initial program 64.0%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 48.8%

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

   if -9.9999999999999994e38 < z < 2.6e99

   1. Initial program 90.1%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 66.8

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

   4. Applied rewrites 66.8%

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

Alternative 10: 51.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+39}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.7e+39) t (if (<= z 2.3e+99) (fma y (/ t a) x) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.7e+39) {
		tmp = t;
	} else if (z <= 2.3e+99) {
		tmp = fma(y, (t / a), x);
	} else {
		tmp = t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.7e+39)
		tmp = t;
	elseif (z <= 2.3e+99)
		tmp = fma(y, Float64(t / a), x);
	else
		tmp = t;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.7e+39], t, If[LessEqual[z, 2.3e+99], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -3.70000000000000012e39 or 2.30000000000000019e99 < z

   1. Initial program 63.9%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 48.9%

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

   if -3.70000000000000012e39 < z < 2.30000000000000019e99

   1. Initial program 90.1%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 66.8

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

   4. Applied rewrites 66.8%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 53.7%

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

Alternative 11: 38.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.1e+15) t (if (<= z 9.2e+78) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+15) {
		tmp = t;
	} else if (z <= 9.2e+78) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.1d+15)) then
        tmp = t
    else if (z <= 9.2d+78) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+15) {
		tmp = t;
	} else if (z <= 9.2e+78) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.1e+15:
		tmp = t
	elif z <= 9.2e+78:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.1e+15)
		tmp = t;
	elseif (z <= 9.2e+78)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.1e+15)
		tmp = t;
	elseif (z <= 9.2e+78)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.1e+15], t, If[LessEqual[z, 9.2e+78], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e15 or 9.2000000000000008e78 < z

   1. Initial program 65.3%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 47.1%

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

   if -1.1e15 < z < 9.2000000000000008e78

   1. Initial program 90.7%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 32.8%

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

Alternative 12: 25.4% accurate, 17.9× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return t;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = t
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return t;
}

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 79.9%

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

2. Taylor expanded in z around inf

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

4. Applied rewrites 25.4%

   \[\leadsto \color{blue}{t} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025119 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))