(/ z0 (* (tan z1) z2))

Percentage Accurate: 95.8% → 99.6%

Time: 52.0s

Alternatives: 3

Speedup: 1.0×

• 79.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\frac{z0}{\tan z1 \cdot z2} \]

FPCore

(FPCore (z0 z1 z2)
  :precision binary64
  (/ z0 (* (tan z1) z2)))

C

double code(double z0, double z1, double z2) {
	return z0 / (tan(z1) * z2);
}

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(z0, z1, z2)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    real(8), intent (in) :: z2
    code = z0 / (tan(z1) * z2)
end function

Java

public static double code(double z0, double z1, double z2) {
	return z0 / (Math.tan(z1) * z2);
}

Python

def code(z0, z1, z2):
	return z0 / (math.tan(z1) * z2)

Julia

function code(z0, z1, z2)
	return Float64(z0 / Float64(tan(z1) * z2))
end

MATLAB

function tmp = code(z0, z1, z2)
	tmp = z0 / (tan(z1) * z2);
end

Wolfram

code[z0_, z1_, z2_] := N[(z0 / N[(N[Tan[z1], $MachinePrecision] * z2), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.8% accurate, 1.0× speedup

Math

\[\frac{z0}{\tan z1 \cdot z2} \]

FPCore

(FPCore (z0 z1 z2)
  :precision binary64
  (/ z0 (* (tan z1) z2)))

C

double code(double z0, double z1, double z2) {
	return z0 / (tan(z1) * z2);
}

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(z0, z1, z2)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    real(8), intent (in) :: z2
    code = z0 / (tan(z1) * z2)
end function

Java

public static double code(double z0, double z1, double z2) {
	return z0 / (Math.tan(z1) * z2);
}

Python

def code(z0, z1, z2):
	return z0 / (math.tan(z1) * z2)

Julia

function code(z0, z1, z2)
	return Float64(z0 / Float64(tan(z1) * z2))
end

MATLAB

function tmp = code(z0, z1, z2)
	tmp = z0 / (tan(z1) * z2);
end

Wolfram

code[z0_, z1_, z2_] := N[(z0 / N[(N[Tan[z1], $MachinePrecision] * z2), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_0 := \tan \left(\left|z1\right|\right)\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z2\right) \cdot \begin{array}{l} \mathbf{if}\;t\_0 \cdot \left|z2\right| \leq \frac{80960901}{202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784}:\\ \;\;\;\;\frac{\frac{z0}{\left|z2\right|}}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{z0}{\sin \left(\left|z1\right|\right) \cdot \left|z2\right|} \cdot \cos \left(\left|z1\right|\right)\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (z0 z1 z2)
  :precision binary64
  (let* ((t_0 (tan (fabs z1))))
  (*
   (copysign 1 z1)
   (*
    (copysign 1 z2)
    (if (<=
         (* t_0 (fabs z2))
         80960901/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784)
      (/ (/ z0 (fabs z2)) t_0)
      (* (/ z0 (* (sin (fabs z1)) (fabs z2))) (cos (fabs z1))))))))

C

double code(double z0, double z1, double z2) {
	double t_0 = tan(fabs(z1));
	double tmp;
	if ((t_0 * fabs(z2)) <= 4e-316) {
		tmp = (z0 / fabs(z2)) / t_0;
	} else {
		tmp = (z0 / (sin(fabs(z1)) * fabs(z2))) * cos(fabs(z1));
	}
	return copysign(1.0, z1) * (copysign(1.0, z2) * tmp);
}

Java

public static double code(double z0, double z1, double z2) {
	double t_0 = Math.tan(Math.abs(z1));
	double tmp;
	if ((t_0 * Math.abs(z2)) <= 4e-316) {
		tmp = (z0 / Math.abs(z2)) / t_0;
	} else {
		tmp = (z0 / (Math.sin(Math.abs(z1)) * Math.abs(z2))) * Math.cos(Math.abs(z1));
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z2) * tmp);
}

Python

def code(z0, z1, z2):
	t_0 = math.tan(math.fabs(z1))
	tmp = 0
	if (t_0 * math.fabs(z2)) <= 4e-316:
		tmp = (z0 / math.fabs(z2)) / t_0
	else:
		tmp = (z0 / (math.sin(math.fabs(z1)) * math.fabs(z2))) * math.cos(math.fabs(z1))
	return math.copysign(1.0, z1) * (math.copysign(1.0, z2) * tmp)

Julia

function code(z0, z1, z2)
	t_0 = tan(abs(z1))
	tmp = 0.0
	if (Float64(t_0 * abs(z2)) <= 4e-316)
		tmp = Float64(Float64(z0 / abs(z2)) / t_0);
	else
		tmp = Float64(Float64(z0 / Float64(sin(abs(z1)) * abs(z2))) * cos(abs(z1)));
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z2) * tmp))
end

MATLAB

function tmp_2 = code(z0, z1, z2)
	t_0 = tan(abs(z1));
	tmp = 0.0;
	if ((t_0 * abs(z2)) <= 4e-316)
		tmp = (z0 / abs(z2)) / t_0;
	else
		tmp = (z0 / (sin(abs(z1)) * abs(z2))) * cos(abs(z1));
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z2) * abs(1.0)) * tmp);
end

Wolfram

code[z0_, z1_, z2_] := Block[{t$95$0 = N[Tan[N[Abs[z1], $MachinePrecision]], $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[z1]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[z2]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[(t$95$0 * N[Abs[z2], $MachinePrecision]), $MachinePrecision], 80960901/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784], N[(N[(z0 / N[Abs[z2], $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], N[(N[(z0 / N[(N[Sin[N[Abs[z1], $MachinePrecision]], $MachinePrecision] * N[Abs[z2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Cos[N[Abs[z1], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (tan.f64 z1) z2) < 3.9999999840454223e-316

   1. Initial program 95.8%

      \[\frac{z0}{\tan z1 \cdot z2} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\tan z1 \cdot z2}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\tan z1 \cdot z2}} \]

      3. *-commutative N/A

         \[\leadsto \frac{z0}{\color{blue}{z2 \cdot \tan z1}} \]

      4. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{z0}{z2}}{\tan z1}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{z0}{z2}}{\tan z1}} \]

      6. lower-/.f64 96.1%

         \[\leadsto \frac{\color{blue}{\frac{z0}{z2}}}{\tan z1} \]

   3. Applied rewrites 96.1%

      \[\leadsto \color{blue}{\frac{\frac{z0}{z2}}{\tan z1}} \]

   if 3.9999999840454223e-316 < (*.f64 (tan.f64 z1) z2)

   1. Initial program 95.8%

      \[\frac{z0}{\tan z1 \cdot z2} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\tan z1 \cdot z2}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\tan z1 \cdot z2}} \]

      3. *-commutative N/A

         \[\leadsto \frac{z0}{\color{blue}{z2 \cdot \tan z1}} \]

      4. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{z0}{z2}}{\tan z1}} \]

      5. lift-tan.f64 N/A

         \[\leadsto \frac{\frac{z0}{z2}}{\color{blue}{\tan z1}} \]

      6. tan-quot N/A

         \[\leadsto \frac{\frac{z0}{z2}}{\color{blue}{\frac{\sin z1}{\cos z1}}} \]

      7. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{\frac{z0}{z2}}{\sin z1} \cdot \cos z1} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{z0}{z2}}{\sin z1} \cdot \cos z1} \]

      9. associate-/l/ N/A

         \[\leadsto \color{blue}{\frac{z0}{z2 \cdot \sin z1}} \cdot \cos z1 \]

      10. *-commutative N/A

          \[\leadsto \frac{z0}{\color{blue}{\sin z1 \cdot z2}} \cdot \cos z1 \]

      11. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{z0}{\sin z1 \cdot z2}} \cdot \cos z1 \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{z0}{\color{blue}{\sin z1 \cdot z2}} \cdot \cos z1 \]

      13. lower-sin.f64 N/A

          \[\leadsto \frac{z0}{\color{blue}{\sin z1} \cdot z2} \cdot \cos z1 \]

      14. lower-cos.f64 95.7%

          \[\leadsto \frac{z0}{\sin z1 \cdot z2} \cdot \color{blue}{\cos z1} \]

   3. Applied rewrites 95.7%

      \[\leadsto \color{blue}{\frac{z0}{\sin z1 \cdot z2} \cdot \cos z1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 99.6% accurate, 0.5× speedup

Math

\[\mathsf{copysign}\left(1, z2\right) \cdot \begin{array}{l} \mathbf{if}\;\left|z2\right| \leq 900:\\ \;\;\;\;\frac{\frac{z0}{\left|z2\right|}}{\tan z1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z0}{\tan z1 \cdot \left|z2\right|}\\ \end{array} \]

FPCore

(FPCore (z0 z1 z2)
  :precision binary64
  (*
 (copysign 1 z2)
 (if (<= (fabs z2) 900)
   (/ (/ z0 (fabs z2)) (tan z1))
   (/ z0 (* (tan z1) (fabs z2))))))

C

double code(double z0, double z1, double z2) {
	double tmp;
	if (fabs(z2) <= 900.0) {
		tmp = (z0 / fabs(z2)) / tan(z1);
	} else {
		tmp = z0 / (tan(z1) * fabs(z2));
	}
	return copysign(1.0, z2) * tmp;
}

Java

public static double code(double z0, double z1, double z2) {
	double tmp;
	if (Math.abs(z2) <= 900.0) {
		tmp = (z0 / Math.abs(z2)) / Math.tan(z1);
	} else {
		tmp = z0 / (Math.tan(z1) * Math.abs(z2));
	}
	return Math.copySign(1.0, z2) * tmp;
}

Python

def code(z0, z1, z2):
	tmp = 0
	if math.fabs(z2) <= 900.0:
		tmp = (z0 / math.fabs(z2)) / math.tan(z1)
	else:
		tmp = z0 / (math.tan(z1) * math.fabs(z2))
	return math.copysign(1.0, z2) * tmp

Julia

function code(z0, z1, z2)
	tmp = 0.0
	if (abs(z2) <= 900.0)
		tmp = Float64(Float64(z0 / abs(z2)) / tan(z1));
	else
		tmp = Float64(z0 / Float64(tan(z1) * abs(z2)));
	end
	return Float64(copysign(1.0, z2) * tmp)
end

MATLAB

function tmp_2 = code(z0, z1, z2)
	tmp = 0.0;
	if (abs(z2) <= 900.0)
		tmp = (z0 / abs(z2)) / tan(z1);
	else
		tmp = z0 / (tan(z1) * abs(z2));
	end
	tmp_2 = (sign(z2) * abs(1.0)) * tmp;
end

Wolfram

code[z0_, z1_, z2_] := N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[z2]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[Abs[z2], $MachinePrecision], 900], N[(N[(z0 / N[Abs[z2], $MachinePrecision]), $MachinePrecision] / N[Tan[z1], $MachinePrecision]), $MachinePrecision], N[(z0 / N[(N[Tan[z1], $MachinePrecision] * N[Abs[z2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z2 < 900

   1. Initial program 95.8%

      \[\frac{z0}{\tan z1 \cdot z2} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\tan z1 \cdot z2}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\tan z1 \cdot z2}} \]

      3. *-commutative N/A

         \[\leadsto \frac{z0}{\color{blue}{z2 \cdot \tan z1}} \]

      4. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{z0}{z2}}{\tan z1}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{z0}{z2}}{\tan z1}} \]

      6. lower-/.f64 96.1%

         \[\leadsto \frac{\color{blue}{\frac{z0}{z2}}}{\tan z1} \]

   3. Applied rewrites 96.1%

      \[\leadsto \color{blue}{\frac{\frac{z0}{z2}}{\tan z1}} \]

   if 900 < z2

   1. Initial program 95.8%

      \[\frac{z0}{\tan z1 \cdot z2} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Reproduce

herbie shell --seed 2025277 -o generate:taylor -o generate:evaluate
(FPCore (z0 z1 z2)
  :name "(/ z0 (* (tan z1) z2))"
  :precision binary64
  (/ z0 (* (tan z1) z2)))