Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1

Percentage Accurate: 96.8% → 99.7%

Time: 1.5min

Alternatives: 14

Speedup: 1.0×

Specification

Math

\[\frac{x - y}{z - y} \cdot t \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.8% accurate, 1.0× speedup

Math

\[\frac{x - y}{z - y} \cdot t \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.7× speedup

Math

\[\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{z - y}\right), y, t, x, t\right) \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (134-z0z1z2z3z4 (/ -1 (- z y)) y t x t))

Derivation

1. Initial program 96.8%

   \[\frac{x - y}{z - y} \cdot t \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. frac-2neg N/A

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

   4. mult-flip N/A

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

   5. *-commutative N/A

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

   6. associate-*l* N/A

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

   7. *-commutative N/A

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

   8. lift--.f64 N/A

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

   9. sub-negate-rev N/A

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

   10. sub-flip N/A

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

   11. distribute-rgt-in N/A

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

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

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

   13. lower-134-z0z1z2z3z4 N/A

       \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{\mathsf{neg}\left(\left(z - y\right)\right)}\right), y, t, x, t\right)} \]

   14. metadata-eval N/A

       \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\color{blue}{\mathsf{neg}\left(-1\right)}}{\mathsf{neg}\left(\left(z - y\right)\right)}\right), y, t, x, t\right) \]

   15. frac-2neg-rev N/A

       \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{z - y}\right)}, y, t, x, t\right) \]

   16. lower-/.f64 99.7%

       \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{-1}{z - y}\right)}, y, t, x, t\right) \]

3. Applied rewrites 99.7%

   \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{z - y}\right), y, t, x, t\right)} \]
4. Add Preprocessing

Alternative 2: 94.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{x}{z - y} \cdot t\\ \mathbf{if}\;t\_1 \leq -500000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \frac{2076918743413931}{20769187434139310514121985316880384}:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 10:\\ \;\;\;\;\frac{y}{y - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ x (- z y)) t)))
  (if (<= t_1 -500000000)
    t_2
    (if (<= t_1 2076918743413931/20769187434139310514121985316880384)
      (* (/ (- x y) z) t)
      (if (<= t_1 10) (* (/ y (- y z)) t) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x / (z - y)) * t;
	double tmp;
	if (t_1 <= -500000000.0) {
		tmp = t_2;
	} else if (t_1 <= 1e-19) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 10.0) {
		tmp = (y / (y - z)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (x / (z - y)) * t
    if (t_1 <= (-500000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 1d-19) then
        tmp = ((x - y) / z) * t
    else if (t_1 <= 10.0d0) then
        tmp = (y / (y - z)) * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x / (z - y)) * t;
	double tmp;
	if (t_1 <= -500000000.0) {
		tmp = t_2;
	} else if (t_1 <= 1e-19) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 10.0) {
		tmp = (y / (y - z)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (x / (z - y)) * t
	tmp = 0
	if t_1 <= -500000000.0:
		tmp = t_2
	elif t_1 <= 1e-19:
		tmp = ((x - y) / z) * t
	elif t_1 <= 10.0:
		tmp = (y / (y - z)) * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(x / Float64(z - y)) * t)
	tmp = 0.0
	if (t_1 <= -500000000.0)
		tmp = t_2;
	elseif (t_1 <= 1e-19)
		tmp = Float64(Float64(Float64(x - y) / z) * t);
	elseif (t_1 <= 10.0)
		tmp = Float64(Float64(y / Float64(y - z)) * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (x / (z - y)) * t;
	tmp = 0.0;
	if (t_1 <= -500000000.0)
		tmp = t_2;
	elseif (t_1 <= 1e-19)
		tmp = ((x - y) / z) * t;
	elseif (t_1 <= 10.0)
		tmp = (y / (y - z)) * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -500000000], t$95$2, If[LessEqual[t$95$1, 2076918743413931/20769187434139310514121985316880384], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 10], N[(N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -5e8 or 10 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 53.1%

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

   4. Applied rewrites 53.1%

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

   if -5e8 < (/.f64 (-.f64 x y) (-.f64 z y)) < 9.9999999999999998e-20

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 50.6%

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

   if 9.9999999999999998e-20 < (/.f64 (-.f64 x y) (-.f64 z y)) < 10

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. metadata-eval N/A

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

      10. frac-2neg-rev N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lower--.f64 84.6%

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

   3. Applied rewrites 84.6%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 45.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-/.f64 N/A

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

      7. frac-2neg N/A

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

      8. metadata-eval N/A

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

      9. mult-flip-rev N/A

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

      10. lower-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lower--.f64 54.1%

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

   8. Applied rewrites 54.1%

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

Alternative 3: 92.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{x}{z - y} \cdot t\\ \mathbf{if}\;t\_1 \leq \frac{-348449143727041}{174224571863520493293247799005065324265472}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \frac{2076918743413931}{20769187434139310514121985316880384}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;t\_1 \leq 10:\\ \;\;\;\;\frac{y}{y - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ x (- z y)) t)))
  (if (<=
       t_1
       -348449143727041/174224571863520493293247799005065324265472)
    t_2
    (if (<= t_1 2076918743413931/20769187434139310514121985316880384)
      (/ (* t (- x y)) z)
      (if (<= t_1 10) (* (/ y (- y z)) t) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x / (z - y)) * t;
	double tmp;
	if (t_1 <= -2e-27) {
		tmp = t_2;
	} else if (t_1 <= 1e-19) {
		tmp = (t * (x - y)) / z;
	} else if (t_1 <= 10.0) {
		tmp = (y / (y - z)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (x / (z - y)) * t
    if (t_1 <= (-2d-27)) then
        tmp = t_2
    else if (t_1 <= 1d-19) then
        tmp = (t * (x - y)) / z
    else if (t_1 <= 10.0d0) then
        tmp = (y / (y - z)) * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x / (z - y)) * t;
	double tmp;
	if (t_1 <= -2e-27) {
		tmp = t_2;
	} else if (t_1 <= 1e-19) {
		tmp = (t * (x - y)) / z;
	} else if (t_1 <= 10.0) {
		tmp = (y / (y - z)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (x / (z - y)) * t
	tmp = 0
	if t_1 <= -2e-27:
		tmp = t_2
	elif t_1 <= 1e-19:
		tmp = (t * (x - y)) / z
	elif t_1 <= 10.0:
		tmp = (y / (y - z)) * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(x / Float64(z - y)) * t)
	tmp = 0.0
	if (t_1 <= -2e-27)
		tmp = t_2;
	elseif (t_1 <= 1e-19)
		tmp = Float64(Float64(t * Float64(x - y)) / z);
	elseif (t_1 <= 10.0)
		tmp = Float64(Float64(y / Float64(y - z)) * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (x / (z - y)) * t;
	tmp = 0.0;
	if (t_1 <= -2e-27)
		tmp = t_2;
	elseif (t_1 <= 1e-19)
		tmp = (t * (x - y)) / z;
	elseif (t_1 <= 10.0)
		tmp = (y / (y - z)) * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -348449143727041/174224571863520493293247799005065324265472], t$95$2, If[LessEqual[t$95$1, 2076918743413931/20769187434139310514121985316880384], N[(N[(t * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 10], N[(N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -2.0000000000000001e-27 or 10 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 53.1%

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

   4. Applied rewrites 53.1%

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

   if -2.0000000000000001e-27 < (/.f64 (-.f64 x y) (-.f64 z y)) < 9.9999999999999998e-20

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 47.9%

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

   4. Applied rewrites 47.9%

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

   if 9.9999999999999998e-20 < (/.f64 (-.f64 x y) (-.f64 z y)) < 10

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. metadata-eval N/A

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

      10. frac-2neg-rev N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lower--.f64 84.6%

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

   3. Applied rewrites 84.6%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 45.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-/.f64 N/A

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

      7. frac-2neg N/A

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

      8. metadata-eval N/A

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

      9. mult-flip-rev N/A

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

      10. lower-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lower--.f64 54.1%

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

   8. Applied rewrites 54.1%

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

Alternative 4: 92.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq \frac{2028240960365167}{5070602400912917605986812821504}:\\ \;\;\;\;\frac{t}{z - y} \cdot \left(x - y\right)\\ \mathbf{elif}\;t\_1 \leq 10:\\ \;\;\;\;\frac{y}{y - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (/ (- x y) (- z y))))
  (if (<= t_1 2028240960365167/5070602400912917605986812821504)
    (* (/ t (- z y)) (- x y))
    (if (<= t_1 10) (* (/ y (- y z)) t) (* (/ x (- z y)) t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 4e-16) {
		tmp = (t / (z - y)) * (x - y);
	} else if (t_1 <= 10.0) {
		tmp = (y / (y - z)) * t;
	} else {
		tmp = (x / (z - y)) * 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)
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) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= 4d-16) then
        tmp = (t / (z - y)) * (x - y)
    else if (t_1 <= 10.0d0) then
        tmp = (y / (y - z)) * t
    else
        tmp = (x / (z - y)) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 4e-16) {
		tmp = (t / (z - y)) * (x - y);
	} else if (t_1 <= 10.0) {
		tmp = (y / (y - z)) * t;
	} else {
		tmp = (x / (z - y)) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= 4e-16:
		tmp = (t / (z - y)) * (x - y)
	elif t_1 <= 10.0:
		tmp = (y / (y - z)) * t
	else:
		tmp = (x / (z - y)) * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 4e-16)
		tmp = Float64(Float64(t / Float64(z - y)) * Float64(x - y));
	elseif (t_1 <= 10.0)
		tmp = Float64(Float64(y / Float64(y - z)) * t);
	else
		tmp = Float64(Float64(x / Float64(z - y)) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= 4e-16)
		tmp = (t / (z - y)) * (x - y);
	elseif (t_1 <= 10.0)
		tmp = (y / (y - z)) * t;
	else
		tmp = (x / (z - y)) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2028240960365167/5070602400912917605986812821504], N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 10], N[(N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 3.9999999999999999e-16

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. mult-flip N/A

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

      9. lower-/.f64 84.8%

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

   3. Applied rewrites 84.8%

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

   if 3.9999999999999999e-16 < (/.f64 (-.f64 x y) (-.f64 z y)) < 10

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. metadata-eval N/A

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

      10. frac-2neg-rev N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lower--.f64 84.6%

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

   3. Applied rewrites 84.6%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 45.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-/.f64 N/A

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

      7. frac-2neg N/A

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

      8. metadata-eval N/A

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

      9. mult-flip-rev N/A

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

      10. lower-/.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lower--.f64 54.1%

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

   8. Applied rewrites 54.1%

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

   if 10 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 53.1%

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

   4. Applied rewrites 53.1%

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

Alternative 5: 92.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{x}{z - y} \cdot t\\ \mathbf{if}\;t\_1 \leq \frac{-348449143727041}{174224571863520493293247799005065324265472}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \frac{4722366482869645}{4722366482869645213696}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;t\_1 \leq 10:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ x (- z y)) t)))
  (if (<=
       t_1
       -348449143727041/174224571863520493293247799005065324265472)
    t_2
    (if (<= t_1 4722366482869645/4722366482869645213696)
      (/ (* t (- x y)) z)
      (if (<= t_1 10) t t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x / (z - y)) * t;
	double tmp;
	if (t_1 <= -2e-27) {
		tmp = t_2;
	} else if (t_1 <= 1e-6) {
		tmp = (t * (x - y)) / z;
	} else if (t_1 <= 10.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (x / (z - y)) * t
    if (t_1 <= (-2d-27)) then
        tmp = t_2
    else if (t_1 <= 1d-6) then
        tmp = (t * (x - y)) / z
    else if (t_1 <= 10.0d0) then
        tmp = t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x / (z - y)) * t;
	double tmp;
	if (t_1 <= -2e-27) {
		tmp = t_2;
	} else if (t_1 <= 1e-6) {
		tmp = (t * (x - y)) / z;
	} else if (t_1 <= 10.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (x / (z - y)) * t
	tmp = 0
	if t_1 <= -2e-27:
		tmp = t_2
	elif t_1 <= 1e-6:
		tmp = (t * (x - y)) / z
	elif t_1 <= 10.0:
		tmp = t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(x / Float64(z - y)) * t)
	tmp = 0.0
	if (t_1 <= -2e-27)
		tmp = t_2;
	elseif (t_1 <= 1e-6)
		tmp = Float64(Float64(t * Float64(x - y)) / z);
	elseif (t_1 <= 10.0)
		tmp = t;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (x / (z - y)) * t;
	tmp = 0.0;
	if (t_1 <= -2e-27)
		tmp = t_2;
	elseif (t_1 <= 1e-6)
		tmp = (t * (x - y)) / z;
	elseif (t_1 <= 10.0)
		tmp = t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -348449143727041/174224571863520493293247799005065324265472], t$95$2, If[LessEqual[t$95$1, 4722366482869645/4722366482869645213696], N[(N[(t * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 10], t, t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -2.0000000000000001e-27 or 10 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 53.1%

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

   4. Applied rewrites 53.1%

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

   if -2.0000000000000001e-27 < (/.f64 (-.f64 x y) (-.f64 z y)) < 9.9999999999999995e-7

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 47.9%

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

   4. Applied rewrites 47.9%

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

   if 9.9999999999999995e-7 < (/.f64 (-.f64 x y) (-.f64 z y)) < 10

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 35.1%

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

Alternative 6: 90.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t}{z - y} \cdot x\\ \mathbf{if}\;t\_1 \leq \frac{-348449143727041}{174224571863520493293247799005065324265472}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \frac{4722366482869645}{4722366482869645213696}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;t\_1 \leq 50:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ t (- z y)) x)))
  (if (<=
       t_1
       -348449143727041/174224571863520493293247799005065324265472)
    t_2
    (if (<= t_1 4722366482869645/4722366482869645213696)
      (/ (* t (- x y)) z)
      (if (<= t_1 50) t t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / (z - y)) * x;
	double tmp;
	if (t_1 <= -2e-27) {
		tmp = t_2;
	} else if (t_1 <= 1e-6) {
		tmp = (t * (x - y)) / z;
	} else if (t_1 <= 50.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (t / (z - y)) * x
    if (t_1 <= (-2d-27)) then
        tmp = t_2
    else if (t_1 <= 1d-6) then
        tmp = (t * (x - y)) / z
    else if (t_1 <= 50.0d0) then
        tmp = t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / (z - y)) * x;
	double tmp;
	if (t_1 <= -2e-27) {
		tmp = t_2;
	} else if (t_1 <= 1e-6) {
		tmp = (t * (x - y)) / z;
	} else if (t_1 <= 50.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (t / (z - y)) * x
	tmp = 0
	if t_1 <= -2e-27:
		tmp = t_2
	elif t_1 <= 1e-6:
		tmp = (t * (x - y)) / z
	elif t_1 <= 50.0:
		tmp = t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(t / Float64(z - y)) * x)
	tmp = 0.0
	if (t_1 <= -2e-27)
		tmp = t_2;
	elseif (t_1 <= 1e-6)
		tmp = Float64(Float64(t * Float64(x - y)) / z);
	elseif (t_1 <= 50.0)
		tmp = t;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (t / (z - y)) * x;
	tmp = 0.0;
	if (t_1 <= -2e-27)
		tmp = t_2;
	elseif (t_1 <= 1e-6)
		tmp = (t * (x - y)) / z;
	elseif (t_1 <= 50.0)
		tmp = t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$1, -348449143727041/174224571863520493293247799005065324265472], t$95$2, If[LessEqual[t$95$1, 4722366482869645/4722366482869645213696], N[(N[(t * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 50], t, t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -2.0000000000000001e-27 or 50 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 50.3%

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

   4. Applied rewrites 50.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 50.4%

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

   6. Applied rewrites 50.4%

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

   if -2.0000000000000001e-27 < (/.f64 (-.f64 x y) (-.f64 z y)) < 9.9999999999999995e-7

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 47.9%

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

   4. Applied rewrites 47.9%

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

   if 9.9999999999999995e-7 < (/.f64 (-.f64 x y) (-.f64 z y)) < 50

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 35.1%

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

Alternative 7: 80.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t}{z - y} \cdot x\\ \mathbf{if}\;t\_1 \leq \frac{2076918743413931}{20769187434139310514121985316880384}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 50:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ t (- z y)) x)))
  (if (<= t_1 2076918743413931/20769187434139310514121985316880384)
    t_2
    (if (<= t_1 50) t t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / (z - y)) * x;
	double tmp;
	if (t_1 <= 1e-19) {
		tmp = t_2;
	} else if (t_1 <= 50.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (t / (z - y)) * x
    if (t_1 <= 1d-19) then
        tmp = t_2
    else if (t_1 <= 50.0d0) then
        tmp = t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / (z - y)) * x;
	double tmp;
	if (t_1 <= 1e-19) {
		tmp = t_2;
	} else if (t_1 <= 50.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (t / (z - y)) * x
	tmp = 0
	if t_1 <= 1e-19:
		tmp = t_2
	elif t_1 <= 50.0:
		tmp = t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(t / Float64(z - y)) * x)
	tmp = 0.0
	if (t_1 <= 1e-19)
		tmp = t_2;
	elseif (t_1 <= 50.0)
		tmp = t;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (t / (z - y)) * x;
	tmp = 0.0;
	if (t_1 <= 1e-19)
		tmp = t_2;
	elseif (t_1 <= 50.0)
		tmp = t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$1, 2076918743413931/20769187434139310514121985316880384], t$95$2, If[LessEqual[t$95$1, 50], t, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 9.9999999999999998e-20 or 50 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 50.3%

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

   4. Applied rewrites 50.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 50.4%

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

   6. Applied rewrites 50.4%

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

   if 9.9999999999999998e-20 < (/.f64 (-.f64 x y) (-.f64 z y)) < 50

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 35.1%

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

Alternative 8: 70.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{x}{z} \cdot t\\ \mathbf{if}\;t\_1 \leq \frac{2076918743413931}{20769187434139310514121985316880384}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ x z) t)))
  (if (<= t_1 2076918743413931/20769187434139310514121985316880384)
    t_2
    (if (<= t_1 10) t t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x / z) * t;
	double tmp;
	if (t_1 <= 1e-19) {
		tmp = t_2;
	} else if (t_1 <= 10.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (x / z) * t
    if (t_1 <= 1d-19) then
        tmp = t_2
    else if (t_1 <= 10.0d0) then
        tmp = t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x / z) * t;
	double tmp;
	if (t_1 <= 1e-19) {
		tmp = t_2;
	} else if (t_1 <= 10.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (x / z) * t
	tmp = 0
	if t_1 <= 1e-19:
		tmp = t_2
	elif t_1 <= 10.0:
		tmp = t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(x / z) * t)
	tmp = 0.0
	if (t_1 <= 1e-19)
		tmp = t_2;
	elseif (t_1 <= 10.0)
		tmp = t;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (x / z) * t;
	tmp = 0.0;
	if (t_1 <= 1e-19)
		tmp = t_2;
	elseif (t_1 <= 10.0)
		tmp = t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, 2076918743413931/20769187434139310514121985316880384], t$95$2, If[LessEqual[t$95$1, 10], t, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 9.9999999999999998e-20 or 10 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 50.6%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 40.2%

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

   7. Applied rewrites 40.2%

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

   if 9.9999999999999998e-20 < (/.f64 (-.f64 x y) (-.f64 z y)) < 10

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 35.1%

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

Alternative 9: 68.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq \frac{2076918743413931}{20769187434139310514121985316880384}:\\ \;\;\;\;\frac{t}{z} \cdot x\\ \mathbf{elif}\;t\_1 \leq 10:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (/ (- x y) (- z y))))
  (if (<= t_1 2076918743413931/20769187434139310514121985316880384)
    (* (/ t z) x)
    (if (<= t_1 10) t (/ (* t x) z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 1e-19) {
		tmp = (t / z) * x;
	} else if (t_1 <= 10.0) {
		tmp = t;
	} else {
		tmp = (t * x) / z;
	}
	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)
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) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= 1d-19) then
        tmp = (t / z) * x
    else if (t_1 <= 10.0d0) then
        tmp = t
    else
        tmp = (t * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 1e-19) {
		tmp = (t / z) * x;
	} else if (t_1 <= 10.0) {
		tmp = t;
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= 1e-19:
		tmp = (t / z) * x
	elif t_1 <= 10.0:
		tmp = t
	else:
		tmp = (t * x) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 1e-19)
		tmp = Float64(Float64(t / z) * x);
	elseif (t_1 <= 10.0)
		tmp = t;
	else
		tmp = Float64(Float64(t * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= 1e-19)
		tmp = (t / z) * x;
	elseif (t_1 <= 10.0)
		tmp = t;
	else
		tmp = (t * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2076918743413931/20769187434139310514121985316880384], N[(N[(t / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 10], t, N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 9.9999999999999998e-20

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 38.2%

         \[\leadsto \frac{t \cdot x}{z} \]

   4. Applied rewrites 38.2%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mult-flip-rev N/A

         \[\leadsto \frac{t}{z} \cdot x \]

      9. lower-/.f64 38.2%

         \[\leadsto \frac{t}{z} \cdot x \]

   6. Applied rewrites 38.2%

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

   if 9.9999999999999998e-20 < (/.f64 (-.f64 x y) (-.f64 z y)) < 10

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 35.1%

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

   if 10 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 38.2%

         \[\leadsto \frac{t \cdot x}{z} \]

   4. Applied rewrites 38.2%

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

Alternative 10: 68.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t}{z} \cdot x\\ \mathbf{if}\;t\_1 \leq \frac{2076918743413931}{20769187434139310514121985316880384}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 50:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ t z) x)))
  (if (<= t_1 2076918743413931/20769187434139310514121985316880384)
    t_2
    (if (<= t_1 50) t t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / z) * x;
	double tmp;
	if (t_1 <= 1e-19) {
		tmp = t_2;
	} else if (t_1 <= 50.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (t / z) * x
    if (t_1 <= 1d-19) then
        tmp = t_2
    else if (t_1 <= 50.0d0) then
        tmp = t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / z) * x;
	double tmp;
	if (t_1 <= 1e-19) {
		tmp = t_2;
	} else if (t_1 <= 50.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (t / z) * x
	tmp = 0
	if t_1 <= 1e-19:
		tmp = t_2
	elif t_1 <= 50.0:
		tmp = t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(t / z) * x)
	tmp = 0.0
	if (t_1 <= 1e-19)
		tmp = t_2;
	elseif (t_1 <= 50.0)
		tmp = t;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (t / z) * x;
	tmp = 0.0;
	if (t_1 <= 1e-19)
		tmp = t_2;
	elseif (t_1 <= 50.0)
		tmp = t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t / z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$1, 2076918743413931/20769187434139310514121985316880384], t$95$2, If[LessEqual[t$95$1, 50], t, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 9.9999999999999998e-20 or 50 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 38.2%

         \[\leadsto \frac{t \cdot x}{z} \]

   4. Applied rewrites 38.2%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mult-flip-rev N/A

         \[\leadsto \frac{t}{z} \cdot x \]

      9. lower-/.f64 38.2%

         \[\leadsto \frac{t}{z} \cdot x \]

   6. Applied rewrites 38.2%

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

   if 9.9999999999999998e-20 < (/.f64 (-.f64 x y) (-.f64 z y)) < 50

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 35.1%

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

Alternative 11: 39.1% accurate, 0.1× speedup

Math

\[\mathsf{copysign}\left(1, t\right) \cdot \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \cdot \left|t\right| \leq \frac{5265614583427859}{105312291668557186697918027683670432318895095400549111254310977536}:\\ \;\;\;\;\frac{\left|t\right| \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|t\right|}{y} \cdot y\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (*
 (copysign 1 t)
 (if (<=
      (* (/ (- x y) (- z y)) (fabs t))
      5265614583427859/105312291668557186697918027683670432318895095400549111254310977536)
   (/ (* (fabs t) y) y)
   (* (/ (fabs t) y) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((((x - y) / (z - y)) * fabs(t)) <= 5e-50) {
		tmp = (fabs(t) * y) / y;
	} else {
		tmp = (fabs(t) / y) * y;
	}
	return copysign(1.0, t) * tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((((x - y) / (z - y)) * Math.abs(t)) <= 5e-50) {
		tmp = (Math.abs(t) * y) / y;
	} else {
		tmp = (Math.abs(t) / y) * y;
	}
	return Math.copySign(1.0, t) * tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (((x - y) / (z - y)) * math.fabs(t)) <= 5e-50:
		tmp = (math.fabs(t) * y) / y
	else:
		tmp = (math.fabs(t) / y) * y
	return math.copysign(1.0, t) * tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(Float64(x - y) / Float64(z - y)) * abs(t)) <= 5e-50)
		tmp = Float64(Float64(abs(t) * y) / y);
	else
		tmp = Float64(Float64(abs(t) / y) * y);
	end
	return Float64(copysign(1.0, t) * tmp)
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((((x - y) / (z - y)) * abs(t)) <= 5e-50)
		tmp = (abs(t) * y) / y;
	else
		tmp = (abs(t) / y) * y;
	end
	tmp_2 = (sign(t) * abs(1.0)) * tmp;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[(N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision] * N[Abs[t], $MachinePrecision]), $MachinePrecision], 5265614583427859/105312291668557186697918027683670432318895095400549111254310977536], N[(N[(N[Abs[t], $MachinePrecision] * y), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[Abs[t], $MachinePrecision] / y), $MachinePrecision] * y), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t) < 4.9999999999999997e-50

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. metadata-eval N/A

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

      10. frac-2neg-rev N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lower--.f64 84.6%

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

   3. Applied rewrites 84.6%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 45.1%

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

   6. Applied rewrites 45.1%

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

   7. Taylor expanded in x around 0

      \[\leadsto \frac{t \cdot y}{y} \]
   8. Step-by-step derivation

   9. Applied rewrites 31.0%

      \[\leadsto \frac{t \cdot y}{y} \]

   if 4.9999999999999997e-50 < (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. metadata-eval N/A

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

      10. frac-2neg-rev N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lower--.f64 84.6%

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

   3. Applied rewrites 84.6%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 45.1%

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

   6. Applied rewrites 45.1%

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

   7. Taylor expanded in x around 0

      \[\leadsto \frac{t \cdot y}{y} \]
   8. Step-by-step derivation

   9. Applied rewrites 31.0%

      \[\leadsto \frac{t \cdot y}{y} \]
   10. Step-by-step derivation

       1. lift--.f64 N/A

          \[\leadsto \frac{t \cdot y}{y} \]

       2. lift-/.f64 N/A

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

       3. *-commutative N/A

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

       4. lift-/.f64 N/A

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

       5. frac-2neg N/A

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

       6. metadata-eval N/A

          \[\leadsto \frac{t \cdot y}{y} \]

       7. mult-flip-rev N/A

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

       8. associate-*l/ N/A

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

       9. distribute-frac-neg2 N/A

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

       10. distribute-frac-neg N/A

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

       11. sub-negate-rev N/A

           \[\leadsto \frac{t \cdot y}{y} \]

       12. lift--.f64 31.0%

           \[\leadsto \frac{t \cdot y}{y} \]

       13. lift-/.f64 N/A

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

       14. mult-flip N/A

           \[\leadsto \left(t \cdot y\right) \cdot \color{blue}{\frac{1}{y}} \]

       15. lift-*.f64 N/A

           \[\leadsto \left(t \cdot y\right) \cdot \frac{\color{blue}{1}}{y} \]

       16. *-commutative N/A

           \[\leadsto \left(y \cdot t\right) \cdot \frac{\color{blue}{1}}{y} \]

       17. associate-*l* N/A

           \[\leadsto y \cdot \color{blue}{\left(t \cdot \frac{1}{y}\right)} \]

       18. *-commutative N/A

           \[\leadsto \left(t \cdot \frac{1}{y}\right) \cdot \color{blue}{y} \]

       19. lower-*.f64 N/A

           \[\leadsto \left(t \cdot \frac{1}{y}\right) \cdot \color{blue}{y} \]

       20. mult-flip-rev N/A

           \[\leadsto \frac{t}{y} \cdot y \]

       21. lower-/.f64 29.5%

           \[\leadsto \frac{t}{y} \cdot y \]

   11. Applied rewrites 29.5%

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

Alternative 12: 38.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq \frac{1942668892225729}{1942668892225729070919461906823518906642406839052139521251812409738904285205208498176}:\\ \;\;\;\;\frac{t \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (if (<=
     (/ (- x y) (- z y))
     1942668892225729/1942668892225729070919461906823518906642406839052139521251812409738904285205208498176)
  (/ (* t y) y)
  t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x - y) / (z - y)) <= 1e-69) {
		tmp = (t * y) / y;
	} 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)
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) :: tmp
    if (((x - y) / (z - y)) <= 1d-69) then
        tmp = (t * y) / y
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x - y) / (z - y)) <= 1e-69) {
		tmp = (t * y) / y;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x - y) / (z - y)) <= 1e-69:
		tmp = (t * y) / y
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x - y) / Float64(z - y)) <= 1e-69)
		tmp = Float64(Float64(t * y) / y);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x - y) / (z - y)) <= 1e-69)
		tmp = (t * y) / y;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], 1942668892225729/1942668892225729070919461906823518906642406839052139521251812409738904285205208498176], N[(N[(t * y), $MachinePrecision] / y), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 9.9999999999999996e-70

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. mult-flip N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. metadata-eval N/A

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

      10. frac-2neg-rev N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lower--.f64 84.6%

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

   3. Applied rewrites 84.6%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 45.1%

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

   6. Applied rewrites 45.1%

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

   7. Taylor expanded in x around 0

      \[\leadsto \frac{t \cdot y}{y} \]
   8. Step-by-step derivation

   9. Applied rewrites 31.0%

      \[\leadsto \frac{t \cdot y}{y} \]

   if 9.9999999999999996e-70 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 35.1%

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

Alternative 13: 35.1% accurate, 23.0× speedup

Math

\[t \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.8%

   \[\frac{x - y}{z - y} \cdot t \]

2. Taylor expanded in y around inf

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

4. Applied rewrites 35.1%

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

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64
  (* (/ (- x y) (- z y)) t))