SynthBasics:moogVCF from YampaSynth-0.2

Average Error: 4.7 → 1.9

Time: 16.1s

Precision: binary64

Cost: 13632

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

def code(x, y, z, t):
	return x + ((y * z) * (math.tanh((t / y)) - math.tanh((x / y))))

↓

def code(x, y, z, t):
	return x + (y * (z * (math.tanh((t / y)) - math.tanh((x / y)))))

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	4.7
Target	1.9
Herbie	1.9

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

Derivation

1. Initial program 4.7

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

2. Applied egg-rr 1.9

   \[\leadsto x + \color{blue}{\left(0 + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\right)} \]

3. Final simplification 1.9

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

Alternatives

Alternative 1
Error	2.2
Cost	41032

\[\begin{array}{l} t_1 := z \cdot \left(t - x\right)\\ t_2 := x + \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot \left(y \cdot z\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	12.8
Cost	7760

\[\begin{array}{l} t_1 := x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right)\\ t_2 := x + z \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -9.158448293998407 \cdot 10^{+81}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.021412497819837 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 16224016139189028:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	12.6
Cost	7760

\[\begin{array}{l} t_1 := x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \frac{x}{y}\right)\right)\\ \mathbf{if}\;x \leq -1.7715089082217477 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.327277239546644 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.0990637036197777 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.60917067771279 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Error	11.8
Cost	7760

\[\begin{array}{l} t_1 := \tanh \left(\frac{t}{y}\right) - \frac{x}{y}\\ \mathbf{if}\;x \leq -1.7715089082217477 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.887156664127385 \cdot 10^{-53}:\\ \;\;\;\;x + z \cdot \left(y \cdot t_1\right)\\ \mathbf{elif}\;x \leq 2.0990637036197777 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.60917067771279 \cdot 10^{+94}:\\ \;\;\;\;x + y \cdot \left(z \cdot t_1\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Error	15.7
Cost	1100

\[\begin{array}{l} t_1 := x + z \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -1.8796762797127602 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.1378554762560274 \cdot 10^{+35}:\\ \;\;\;\;x + z \cdot t\\ \mathbf{elif}\;y \leq -0.00030247103939522294:\\ \;\;\;\;x + \frac{\left(y \cdot z\right) \cdot \left(t - x\right)}{y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+130}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	15.7
Cost	976

\[\begin{array}{l} t_1 := x + z \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -1.8796762797127602 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.1378554762560274 \cdot 10^{+35}:\\ \;\;\;\;x + z \cdot t\\ \mathbf{elif}\;y \leq -0.00030247103939522294:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+130}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	20.9
Cost	848

\[\begin{array}{l} t_1 := x - x \cdot z\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+295}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{+231}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;y \leq -1.8796762797127602 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+141}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	21.2
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{+212}:\\ \;\;\;\;z \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+141}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \]

Alternative 9
Error	18.3
Cost	584

\[\begin{array}{l} t_1 := x + z \cdot t\\ \mathbf{if}\;y \leq -15739998423.077587:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+124}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	23.0
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -9.978559651284736 \cdot 10^{-161}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.102253074214164 \cdot 10^{-213}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Error	22.7
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022298 
(FPCore (x y z t)
  :name "SynthBasics:moogVCF from YampaSynth-0.2"
  :precision binary64

  :herbie-target
  (+ x (* y (* z (- (tanh (/ t y)) (tanh (/ x y))))))

  (+ x (* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))))